Showing papers on "Coupled map lattice published in 2001"
TL;DR: Numerical simulations demonstrate the feasibility of the proposed model system that allows communication of spatiotemporal information using an optical chaotic carrier waveform, and the benefit of the parallelism of information transfer with optical wave fronts.
Abstract: We propose a model system that allows communication of spatiotemporal information using an optical chaotic carrier waveform. The system is based on broad-area nonlinear optical ring cavities, which exhibit spatiotemporal chaos in a wide parameter range. Message recovery is possible through chaotic synchronization between transmitter and receiver. Numerical simulations demonstrate the feasibility of the proposed scheme, and the benefit of the parallelism of information transfer with optical wave fronts.
155 citations
TL;DR: A control law is derived based on the mechanism of projective synchronization of three-dimensional systems and an application is illustrated for the Lorenz system.
Abstract: We show that the scaling factor of projective synchronization in coupled partially linear systems is unpredictable. This gives rise to the difficulty in estimating the state of synchronized dynamics. We therefore propose a control method to manipulate the scaling factor onto any desired value so that the synchronization can be managed in a preferred way. A control law is derived based on the mechanism of projective synchronization of three-dimensional systems and an application is illustrated for the Lorenz system.
120 citations
TL;DR: This work compared the predictions of discrete-state and continuous-state population models and suggested that such lattice effects could be an important component of natural population fluctuations.
Abstract: Animals and many plants are counted in discrete units. The collection of possible values (state space) of population numbers is thus a nonnegative integer lattice. Despite this fact, many mathematical population models assume a continuum of system states. The complex dynamics, such as chaos, often displayed by such continuous-state models have stimulated much ecological research; yet discrete-state models with bounded population size can display only cyclic behavior. Motivated by data from a population experiment, we compared the predictions of discrete-state and continuous-state population models. Neither the discrete- nor continuous-state models completely account for the data. Rather, the observed dynamics are explained by a stochastic blending of the chaotic dynamics predicted by the continuous-state model and the cyclic dynamics predicted by the discrete-state models. We suggest that such lattice effects could be an important component of natural population fluctuations.
88 citations
TL;DR: An invariant manifold based chaos synchronization approach is proposed by using only a partial state of chaotic systems to synchronize the coupled chaotic systems by taking into account the inherent dynamic properties of the chaotic systems.
Abstract: An invariant manifold based chaos synchronization approach is proposed in this letter A novel idea of using only a partial state of chaotic systems to synchronize the coupled chaotic systems is presented by taking into account the inherent dynamic properties of the chaotic systems The effectiveness of the approach and idea is tested on the Lorenz system and the fourth-order Rossler system
88 citations
TL;DR: A model of many symmetrically and locally coupled chaotic oscillators is studied and partial chaotic synchronizations associated with spontaneous spatial ordering are demonstrated.
Abstract: A model of many symmetrically and locally coupled chaotic oscillators is studied. Partial chaotic synchronizations associated with spontaneous spatial ordering are demonstrated. Very rich patterns of the system are revealed, based on partial synchronization analysis. The stabilities of different partially synchronous spatiotemporal structures and some dynamical behaviors of these states are discussed both numerically and analytically.
77 citations
TL;DR: A new method to estimate the spatial cross-correlation function between two species was developed as an integral part of the study and speculated that this spatial lag between the host and parasitoid is the ultimate source of travelling waves.
Abstract: Summary 1. Recent theoretical studies on population synchrony have focused on the role of dispersal, environmental correlation and density dependence in single species. Trophic interactions have received less attention. We explored how trophic interactions affect spatial synchrony. 2. We considered a host‐parasitoid coupled map lattice to understand how the selforganizing spatial patterns generated by such dynamics affect synchrony. In particular, we calculated the spatial correlation functions (SCF) associated with travelling waves, spatial chaos and crystal lattices. 3. Travelling waves were associated with cyclic SCF (called second-order SCF) that differed greatly from those seen in spatial chaos or crystal lattices. Such U-shaped patterns of spatial synchrony, which have not been predicted by single-species models, have been reported recently in real data. Thus, the shape of the SCF can provide a test for trophically generated spatiotemporal dynamics. 4. We also calculated the cross-correlation function between the parasitoid and the host. Relatively high parasitoid mobility resulted in high within-patch synchrony of the dynamics of the two species. However, with relatively high host mobility, the parasitoid dynamics began to lag spatially behind those of the host. 5. We speculated that this spatial lag between the host and parasitoid is the ultimate source of travelling waves, because the spatial cross-correlation in turn affects host dynamics. 6. A new method to estimate the spatial cross-correlation function between two species was developed as an integral part of the study.
75 citations
TL;DR: Evidence is provided for the existence of chaotic dynamics in a neurophysiologically plausible continuum theory of electrocortical activity and it is shown that the set of parameter values supporting chaos within parameter space has positive measure and exhibits fat fractal scaling.
Abstract: Various techniques designed to extract nonlinear characteristics from experimental time series have provided no clear evidence as to whether the electroencephalogram (EEG) is chaotic. Compounding the lack of firm experimental evidence is the paucity of physiologically plausible theories of EEG that are capable of supporting nonlinear and chaotic dynamics. Here we provide evidence for the existence of chaotic dynamics in a neurophysiologically plausible continuum theory of electrocortical activity and show that the set of parameter values supporting chaos within parameter space has positive measure and exhibits fat fractal scaling.
70 citations
TL;DR: A method for the identification of nonlinear coupled map lattices (CML) equations from measured spatio-temporal data is introduced and the resulting models are validated by computing the attractors and the largest Lyapunov exponents.
54 citations
TL;DR: It is shown that the transition from laminar to active behavior in extended chaotic systems can vary from a continuous transition in the universality class of directed percolation with infinitely many absorbing states to what appears as a first-order transition.
Abstract: We show that the transition from laminar to active behavior in extended chaotic systems can vary from a continuous transition in the universality class of directed percolation with infinitely many absorbing states to what appears as a first-order transition. The latter occurs when finite lifetime nonchaotic structures, called "solitons," dominate the dynamics. We illustrate this scenario in an extension of the deterministic Chate-Manneville coupled map lattice model and in a soliton including variant of the stochastic Domany-Kinzel cellular automaton.
42 citations
TL;DR: It is shown that the loss of synchronization for the coherent state and the emergence of subgroups of oscillators with synchronized behavior are two distinct processes, and that the type of behavior that arises after the Loss of total synchronization depends sensitively on the dynamics of the individual map.
Abstract: We study the formation of symmetric (i.e., equally sized) or nearly symmetric clusters in an ensemble of globally coupled, identical chaotic maps. It is shown that the loss of synchronization for the coherent state and the emergence of subgroups of oscillators with synchronized behavior are two distinct processes, and that the type of behavior that arises after the loss of total synchronization depends sensitively on the dynamics of the individual map. For our system of globally coupled logistic maps, symmetric two-cluster formation is found to proceed through a periodic state associated with the stabilization either of an asynchronous period-2 cycle or of an asynchronous period-4 cycle. With further reduction of the coupling strength, each of the principal clustering states undergoes additional bifurcations leading to cycles of higher periodicity or to quasiperiodic and chaotic dynamics. If desynchronization of the coherent chaotic state occurs before the formation of stable clusters becomes possible, high-dimensional chaotic motion is observed in the intermediate parameter interval.
36 citations
TL;DR: In this paper, the statistics of Kolmogorov-Sinai (KS) entropy for a coupled map lattice model are analyzed from the viewpoint of the thermodynamic formalism.
Abstract: The statistics of Kolmogorov–Sinai (KS) entropy for a coupled map lattice model are analyzed from the viewpoint of the thermodynamic formalism. It is shown that the fluctuation of KS entropy for a coupled map lattice model satisfies the large deviation statistics. Also, the probability density of Lyapunov exponents (PDLE) is studied and it is shown that the PDLE gives the measure of the irregularity for the spatio-temporal patterns. Mean Lyapunov exponent is introduced and compared with KS entropy.
TL;DR: A computational model for scene segmentation based on a network of dynamically coupled chaotic maps is proposed, which achieves good performance and transparent dynamics by utilizing one-dimensional chaotic map instead of complex neuron as each element.
Abstract: In this paper, a computational model for scene segmentation based on a network of dynamically coupled chaotic maps is proposed. Time evolutions of chaotic maps that correspond to an object in the given scene are synchronized with one another, while this synchronized evolution is desynchronized with respect to time evolution of chaotic maps corresponding to other objects in the scene. In this model, the coupling range of each active element increases dynamically according to predefined rules until a saturated state is achieved, i.e., locally coupled chaotic maps corresponding to an object in the initial state will be coupled globally in the final state. Consequently, the advantage of both global coupling and local coupling are incorporated in a single scheme. In comparison to continuous models, this proposed model is suitable for computational implementation. Another significant benefit is that the good performance and transparent dynamics of the model are obtained by utilizing one-dimensional chaotic map instead of complex neuron as each element.
TL;DR: A crossover transition from spatially random chaos to spatially ordered chaos with phase locking and orientational equality (for two directions) breaking is a crucial step for establishing the typical spatial order of the rotating wave.
Abstract: A route to typical rotating waves from high-dimensional chaos is investigated in diffusively coupled chaotic R\"ossler oscillators By increasing the coupling from zero, a high-dimensional spatiotemporal chaos changes into a coherent state, which is periodic in time and well ordered in space, through consecutive transitions A crossover transition from spatially random chaos to spatially ordered chaos with phase locking and orientational equality (for two directions) breaking is a crucial step for establishing the typical spatial order of the rotating wave
TL;DR: In this paper, a coupled map lattice corresponding to the spatial prisoner's dilemma game is constructed and studied in the weak diffusion limit, and it is shown that periodic solutions are dense in weak coupling regime and that this system is structurally stable.
Abstract: It is argued that telegraph equation is more suitable than ordinary diffusion equation in modeling reaction diffusion in biological, economic and social systems. Telegraph reaction diffusion (TRD) is studied in one and two spatial dimensions. Some exact and approximate results are obtained. A coupled map lattice (CML) corresponding to the spatial prisoner's dilemma game is constructed and studied in the weak diffusion limit. A formula is derived for Lyapunov exponents and it is shown that periodic solutions are dense in the weak coupling regime and that this system is structurally stable.
TL;DR: There can be a functional relation between time-lagged dynamical variables of the coupled oscillators in wide parameter regimes and this phenomenon is identified: generalized time- lagged synchronization.
Abstract: We investigate, experimentally, synchronization in coupled chaotic oscillators in the presence of large parameter mismatches and identify a different phenomenon: generalized time-lagged synchronization. Specifically, we find that there can be a functional relation between time-lagged dynamical variables of the coupled oscillators in wide parameter regimes.
Book•
01 Jan 2001
TL;DR: In this paper, the authors propose a method to overcome the Antithesis between Determinism and Nondeterminism or between programs and errors in the context of complex systems.
Abstract: 1. Necessity for a Science of Complex Systems.- 1.1 Introduction.- 1.2 Chaos.- 1.3 Chaos and Complexity.- 1.4 How Has Chaos Changed Our Way of Thinking?.- 1.4.1 Dialectic Method to Overcome the Antithesis Between Determinism and Nondeterminism or Between Programs and Errors.- 1.4.2 Dialectic Method to Overcome the Antithesis Between Order and Randomness.- 1.4.3 Beyond the Antithesis Between Reductionism and Holism.- 1.5 Dynamic Many-to-Many Relations and Bio-networks.- 1.5.1 The Necessity of Dynamic Many-to-Many Relations.- 1.5.2 Metabolic Systems, Differentiation, and Development.- 1.5.3 Ecosystems.- 1.5.4 Immune Systems.- 1.5.5 The Brain.- 1.5.6 Rugged Landscapes and Their Problems.- 1.5.7 Conclusion.- 1.6 The Construction of an Artificial (Virtual) World.- 1.7 A Trigger to Emergence.- 1.8 Beyond Top-Down Versus Bottom-Up.- 1.9 Methodology of Study of Complex Systems.- 1.9.1 Constructive Way of Understanding.- 1.9.2 Plural Views.- 1.9.3 Mathematical Anatomy.- 1.9.4 The Problem of Internal Observers.- 2. Observation Problems from an Information-Theoretical Viewpoint.- 2.1 Observation Problems of Chaos.- 2.2 Undecidability and Entire Description.- 2.3 A Demon in Chaos.- 2.4 Chaos in the BZ Reaction.- 2.5 Noise-Induced Order.- 2.6 Could Structural Stability Lead to an Adequate Notion of a Model?.- 2.7 Information Theory of Chaos.- 3. CMLs: Constructive Approach to Spatiotemporal Chaos.- 3.1 From a Descriptive to a Constructive Approach of Nature.- 3.2 Coupled Map Lattice Approach to Spatiotemporal Chaos.- 3.2.1 Spatiotemporal Chaos.- 3.2.2 Introduction to Coupled Map Lattices.- 3.2.3 Comparison with Other Approaches.- 3.3 Phenomenology of Spatiotemporal Chaos in the Diffusively Coupled Logistic Lattice.- 3.3.1 Introduction.- 3.3.2 Frozen Random Patterns and Spatial Bifurcations.- 3.3.3 Pattern Selection with Suppression of Chaos.- 3.3.4 Brownian Motion of Chaotic Defects and Defect Turbulence.- 3.3.5 Spatiotemporal Intermittency (STI).- 3.3.6 Stability of Fully Developed Spatiotemporal Chaos (FDSTC) Sustained by the Supertransients.- 3.3.7 Traveling Waves.- 3.3.8 Supertransients.- 3.4 CML Phenomenology as a Problem of Complex Systems.- 3.5 Phenomenology in Open-Flow Lattices.- 3.5.1 Introduction.- 3.5.2 Spatial Bifurcation to Down-Flow.- 3.5.3 Convective Instability and Spatial Amplification of Fluctuations.- 3.5.4 Phase Diagram.- 3.5.5 Spatial Chaos.- 3.5.6 Selective Amplification of Input.- 3.6 Universality.- 3.7 Theory for Spatiotemporal Chaos.- 3.8 Applications of Coupled Map Lattices.- 3.8.1 Pattern Formation (Spinodal Decomposition).- 3.8.2 Crystal Growth and Boiling.- 3.8.3 Convection.- 3.8.4 Spiral and Traveling Waves in Excitable Media.- 3.8.5 Cloud Dynamics and Geophysics.- 3.8.6 Ecological Systems.- 3.8.7 Evolution.- 3.8.8 Closing Remarks.- 4. Networks of Chaotic Elements.- 4.1 GCM Model.- 4.2 Clustering.- 4.3 Phase Transitions Between Clustering States.- 4.4 Ordered Phase and Cluster Bifurcation.- 4.5 Hierarchical Clustering and Chaotic Itinerancy.- 4.5.1 Partition Complexity.- 4.5.2 Hierarchical Clustering.- 4.5.3 Hierarchical Dynamics.- 4.5.4 Chaotic Itinerancy.- 4.6 Marginal Stability and Information Cascade.- 4.6.1 Marginal Stability.- 4.6.2 Information Cascade.- 4.7 Collective Dynamics.- 4.7.1 Remnant Mean-Field Fluctuation.- 4.7.2 Hidden Coherence.- 4.7.3 Instability of the Fixed Point of the Perron-Frobenius Operator.- 4.7.4 Destruction of Hidden Coherence by Noise and Anomalous Fluctuations.- 4.7.5 Heterogeneous Systems.- 4.7.6 Significance of Collective Dynamics.- 4.8 Universality and Nonuniversality.- 4.8.1 Universality of Clustering and Other Transitions.- 4.8.2 Globally Coupled Tent Map: Novelty Within Universality.- 5. Signifieanee of Coupled Chaotic Systems to Biological Networks.- 5.1 Relevance of Coupled Maps to Biological Information Processing.- 5.2 Application of Coupled Maps to Information Processing.- 5.2.1 Memory to Attractor Mapping and the Switching Process.- 5.2.2 Chaotic Itinerancy and Spontaneous Recall.- 5.2.3 Optimization and Search by Spatiotemporal Chaos as Spatiotemporally Structured Noise.- 5.2.4 Local-Global Transformation by Traveling Waves Information Creation and Transmission by Chaotic Traveling Waves.- 5.2.5 Selective Amplification of Input Signals by the Unidirectionally Coupled Map Lattice.- 5.3 Information Dynamics of a CML with One-Way Coupling.- 5.4 Design of Coupled Maps and Plastic Dynamics.- 5.5 Construction of Dynamic Many-to-Many Logic and Information Processing.- 5.6 Implications to Biological Networks.- 5.6.1 Prototype of Hierarchical Structures.- 5.6.2 Prototype of Diversity and Differentiation.- 5.6.3 Formation and Collapse of Relationships.- 5.6.4 Clustering in Hypercubic Coupled Maps Self-organizing Genetic Algorithms.- 5.6.5 Homeochaos.- 5.6.6 Summing Up.- 6. Chaotic Information Processing in the Brain.- 6.1 Hermeneutics of the Brain.- 6.2 A Brief Comment on Hermeneutics (the Inside and the Outside).- 6.3 A Method for Understanding th e Brain and Mind - Internal Description.- 6.4 Evidence of Chaos in Nervous Systems.- 6.5 The Origin of Neurochaos.- 6.6 The Implications of Stochastic Renewal of Maps.- 6.6.1 Chaotic Game.- 6.6.2 Skew-Product Transformations.- 6.7 A Model for Dynamic Memory.- 6.8 A Model for Dynamically Linking Memories.- 6.9 Significance of Neurochaos.- 6.10 Temporal Coding.- 6.11 Capillary Chaos as a Complex Dynamics.- 6.11.1 Significance of Capillary Pulsation in the Brain Functions.- 6.11.2 Embedding Theorems.- 6.11.3 Experimental Systems.- 6.11.4 Reconstruction of the Dynamics.- 6.11.5 Calculations of Lyapunov Exponents.- 6.11.6 The Condition Dependence.- 6.11.7 Cardiac Chaos.- 6.11.8 Information Structure.- 6.11.9 Implication s of Capillary Chaos.- 7. Conversations with Authors.- 7.1 Concluding Discussions.- 7.2 Questions and Answers.- 7.2.1 The Significance of Models in Complex Systems Research.- 7.2.2 Chaotic Itinerancy.- 7.2.3 New Information Theory and Internal Observation.- References.
TL;DR: In numerical simulations, global and local control is obtained in coupled map lattice systems by the same phase space compression in different situations, and it is found that the functional relationship of control results to control parameters in a certain region is the same as the local dynamics expression of the CML.
Abstract: We present a simple and effective method for controlling spatiotemporal chaos (STC) via phase space compression, by compressing the evolution orbit of the chaotic attractor. In numerical simulations, we obtain global and local control in coupled map lattice (CML) systems by the same phase space compression in different situations, and find that the functional relationship of control results to control parameters in a certain region is the same as the local dynamics expression of the CML. According to the control equation, using different phase space compressions we successfully control a CML exhibiting STC into various desired stable states.
TL;DR: In this article, the authors consider a one-dimensional lattice of expanding antisymmetric maps with nearest neighbor diffusive coupling and show that the mean square magnetization appears to diverge as the coupling parameter grows beyond some critical value.
Abstract: We consider a one-dimensional lattice of expanding antisymmetric maps [−1, 1]→[−1, 1] with nearest neighbor diffusive coupling. For such systems it is known that if the coupling parameter e is small there is unique stationary (in time) state, which is chaotic in space-time. A disputed question is whether such systems can exhibit Ising-type phase transitions as e grows beyond some critical value ec. We present results from computer experiments which give definite indication that such a transition takes place: the mean square magnetization appears to diverge as e approaches some critical value, with a critical exponent around 0.9. We also study other properties of the coupled map system.
TL;DR: It is evident that thresholding is capable of yielding exact limit cycles of varying periods and geometries when implemented at different intervals (even when very infrequent), which suggests a simple and potent mechanism for selecting different regular temporal patterns from chaotic dynamics.
Abstract: We show how stroboscopic threshold mechanisms can be effectively employed to obtain a wide range of stable cyclic behavior from chaotic systems, by simply varying the frequency of control. We demonstrate the success of the scheme in a prototypical one-dimensional map, as well as in a three-dimensional system modeling lasers where the threshold action is implemented on any one of the variables. It is evident that thresholding is capable of yielding exact limit cycles of varying periods and geometries when implemented at different intervals (even when very infrequent). This suggests a simple and potent mechanism for selecting different regular temporal patterns from chaotic dynamics.
TL;DR: In this article, a spatially one dimensional coupled map lattice with a local and unidirectional coupling is introduced, which is studied analytically by a perturbation theory that is valid for small coupling strength.
Abstract: A spatially one dimensional coupled map lattice with a local and unidirectional coupling is introduced. This model is studied analytically by a perturbation theory that is valid for small coupling strength. In parameter space three phases with different ergodic behaviour are observed. Via coarse graining the deterministic model is mapped to a stochastic spin model that can be described by a master equation. Because of the anisotropic coupling non-equilibrium behaviour is found on the coarse grained level. However, the stationary statistical properties of the spin dynamics can still be described with a nearest neighbour Ising model whereby the ordering is predominantly antiferromagnetic.
TL;DR: A survey of the state of the art in the theory of chaotic dynamical systems can be found in this paper, where the most popular methods for stabilizing chaotic behavior and controlling deterministic dynamical system are reviewed.
Abstract: The survey provides a fairly rigorous description of the state of the art in the theory of chaotic dynamical systems. Results pertaining to the onset of chaos in such systems are presented and their main properties are discussed. The most popular methods for stabilizing chaotic behavior and controlling deterministic dynamical systems are reviewed.
TL;DR: In this paper, the dispersion of the nonlinear Schrodinger equation is modified to obtain a model system for which the number of unstable modes remains fixed while the domain size increases.
TL;DR: In this paper, a method for controlling chaotic oscillations in delay differential systems is presented, which is intrinsically heuristic, relies on the capability of predicting the peak (relative maximum) of an output variable from the knowledge of the previous peak.
Abstract: A method for controlling chaotic oscillations in delay differential systems is presented. The method, which is intrinsically heuristic, relies on the capability of predicting the peak (relative maximum) of an output variable from the knowledge of the previous peak. This property, called peak-to-peak dynamics, is owned by several finite-dimensional systems, and crucially relies on the low-dimensionality of the chaotic attractor. In this paper it is shown that even delay-differential systems may display peak-to-peak dynamics, and the conditions giving rise to this property are analyzed. Then, a reduced model (a first-order map) derived via peak-to-peak dynamics is exploited to suppress chaos in favor of a periodic regime.
TL;DR: In this article, the jamming transition from free traffic to oscillatory traffic is investigated with the unidirectionally coupled map lattice model which has the hyperbolic tangent local map.
Abstract: The jamming transition from the free traffic to the oscillatory traffic is investigated with the unidirectionally coupled map lattice model which has the hyperbolic tangent local map. Spatio-temporal structures in the jamming transition are found with the use of numerical simulation. The traffic states are studied for both constant and noisy boundary conditions. We show the phase diagrams of different kinds of congested traffic. It is found that the noise at the boundary has an important effect on the traffic states. The traffic behavior in the coupled map lattice model exhibits a jamming transition similar to that found in the car-following model.
Book•
01 Jan 2001
TL;DR: In this paper, the authors proposed a deterministic nonlinear model for the analysis of chaotic dynamics in a tractors' time-series data, based on the Lorenz equation.
Abstract: Preface. Chapter 1. Introduction. Science and reproducibility. Chaos. Studies of chaos on agricultural systems. Summary of the book. Chapter 2. Deterministic Chaos. Concepts of deterministic chaos. Deterministic dynamical system. May's deterministic chaos. Complexity produced by simplicity. Return map. Period doubling route to chaos. Bifurcation diagram. Feigenbaum number. Discrete dynamical systems. One-dimensional discrete system. Malthusian growth model. Logistic growth model. Self-similarity of the bifurcation structure. Other one-dimensional discrete dynamical systems. Two-dimensional discrete dynamical system. Competition between two species. Prey-predator relationship. Continuous dynamical systems. Chaos of Lorenz System. Lorenz equation. Lorenz attractor. Chaos of Duffing's Equation. Duffing's Equation. Ueda's Chaos Attractor. Chapter 3. Analysis of Chaotic Data. Chaos time-series analysis. Spectral analysis. Delay coordinate embedding. Correlation dimension. Deterministic nonlinear prediction. Reconstruction of dynamics. Concept of prediction. Practice of prediction. Response surface methodology. Return map. Hassell's analysis. RSM analysis. Chapter 4. Numerical Practice on Chaotic Population Dynamics in Plant Communities. Dynamics of a weed community. Life table of a weed community. Density dependence of weeds. Nonlinear dynamics in weed population. Linear dynamical system. Grass-litter dynamics. Chapter 5. Nonlinear Dynamics in Alternate Bearing and Masting of Tree Crops. Introduction. Models of masting and alternate bearing. Isagi's paradigm. Resource budget model. Simulated population dynamics. Two dimensional resource budget model. Reconstruction of dynamics by RSM. Applications to acorn data. Application to citrus dynamics. Controlling chaos and fruit thinning. One dimensional system. Two dimensional system. Formulation of OGY control on the reconstructed dynamics by RSM. Control without noise. Control when the stable point estimation involves errors. Conclusions. Chapter 6. Weed-Tillage Dynamics. Introduction. Basic concept of weed-tillage dynamics. The simplest model. The model incorporating field practice. The model incorporating density effect. Application. The k state variables model. Numerical experiments. Tillage transform parameters. Biological parameters. Results and discussions. Conclusions. Chapter 7. Chaotic Vibrations in Agricultural Machinery. Introduction. Chaos in a vibrating subsoiler. Materials and methods. Correlation dimension. Bifurcation when changing the forcing frequency. Periodic vibration. Period-doubling vibration. Chaotic vibration. Largest lyapunov exponents. Deterministic nonlinear prediction on the time-series of the acceleration. Theoretical investigations of nonlinear dynamics in a farm tractor. Mathematical model of bouncing tractor. Numerical simulations. Periodic vibration. Period doubling vibration. Quasi-periodic vibration. Chaotic vibration. Bifurcation structure. Experimental investigations of non-linear dynamics in a farm tractor. Experimental set up. Experimental bifurcation. Periodic vibrations. Quasi-periodic vibration. Period-doubling/chaotic vibrations. Nonlinear resonance. References. Chapter 8. Nonlinear Time Series Analysis in Piglet Pricing Data. Introduction. Dynamic model of agricultural commodities. Cob-web theorem. Larson's feedback model. Chaos time series analysis on pig cycle. Background of pork production in Japan. Trends of pig price and population. Deterministic nonlinear prediction. Modeling. Prediction. Conclusions. References. Chapter 9. Deterministic Nonlinear Prediction on Diurnal Change in Tangential Strain of Inner Bark for White Birch. Introduction. Experimental method. Spectral analysis of time-series data. Modeling of time-series data. Non-linear dynamic model without considering the external environment (Dynamic Model A). Non-linear dynamic model with consideration of the external environment (Dynamic Model B). Non-linear regression model incorporating temperature. Results of analysis. Results of reconstruction of dynamics. Deterministic nonlinear prediction. Dynamic model of stomatal oscillation and Hopf bifurcation. Conclusions. References. Chapter 10. Spatio-Temporal Dynamics in Arable Land. Introduction. Models of spatio-temporal dynamics. Spatially extended Lotka Volterra model. Coupled map lattice. Identification of locally coupled dynamics. Prediction. Conclusion. References. Chapter 11. Fractal of Arable Land. Fractal of the crop root system. Fractal dimensions of roots. Root system growth models. Fractal of soil pores. Fractal of the soil erosion network. Fractal of field surface irregularity. Conclusion. References. Appendix A. Numerical Analysis of Ordinary Differential Equations by the Runge-Kutta Method. Appendix B. Outline of the Neural Networks.
TL;DR: In this paper, a methodology for the construction of invariant domains in the phase space is developed and applied to the study of pattern formation and inter-layer synchronization in a two-layer bistable coupled map lattice.
TL;DR: A simple method is presented for controlling spatiotemporal chaos in coupled map lattices to a homogeneous state and the stability analysis of the homogeneity state is offered.
Abstract: A simple method is presented for controlling spatiotemporal chaos in coupled map lattices to a homogeneous state This method can be applied to many kinds of models such as coupled map lattices (CML), one-way open CML (the open-flow model), and globally coupled map We offer the stability analysis of the homogeneous state Simple and sufficient conditions are obtained for controlling the above mentioned models Our theoretical results agree well with numerical simulations
TL;DR: An encryption approach to digital communication by using spatiotemporal chaos synchronization is proposed and an example of duplex real-time voice communication between two computer users is described.
Abstract: An encryption approach to digital communication by using spatiotemporal chaos synchronization is proposed. Two one-way coupled map lattice (OCOML) systems driven by a chaotic signal are synchronized. The chaotic outputs of the OCOML systems serve as the encryption and decryption keys and the main secret key is a set of coupling parameters of the OCOML. The advantages of the cryptosystem are its high communication efficiency, higher level of security and easy implementation by software. An example of duplex real-time voice communication between two computer users is described.
TL;DR: The simplest equivariant chaotic dynamics is investigated in terms of its image, i.e., under the 2-->1 mapping allowing one to obtain a projection of the dynamics without any residual symmetry, and the inversion symmetry is deleted.
Abstract: The simplest equivariant chaotic dynamics is investigated in terms of its image, i.e., under the 2-->1 mapping allowing one to obtain a projection of the dynamics without any residual symmetry. The inversion symmetry is therefore deleted. The bifurcation diagram can thus be predicted from the unimodal order although the first-return map computed in the original phase space exhibits three critical points. This feature is the same as the one observed on the Burke and Shaw system although this latter system has a rotation symmetry.