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Journal ArticleDOI

Noise-induced phenomena in a versatile class of prototype dynamical system with time delay

19 Jan 2018-Nonlinear Dynamics (Springer Netherlands)-Vol. 92, Iss: 2, pp 511-529
TL;DR: In this paper, a general class of prototype birhythmic dynamical systems, which can be extensively used to study the generation of complex bifurcation of limit cycles, were investigated under the influences of noise and time delay feedback.
Abstract: This work presents a general class of prototype birhythmic dynamical systems, which can be extensively used to study the generation of complex bifurcation of limit cycles. Using a delay nonlinear Langevin approach, the stationary probability distribution and the escape problem are investigated under the influences of noise and time delay feedback. We discuss a new mechanism for the translocation of the amplitude in which the energy originates from noise. The results indicate that depending on the parameter space the system exhibits a transition from birhythmic to monorhythmic behavior or amplitude death. Besides, results demonstrated that time delay and feedback intensity as well as noise intensity will induce the appearance of stochastic bifurcation. Moreover, a novel finding is that the mean first passage time non-monotonically depends on the noise intensity and the dominant frequency of the oscillation. This finding represents the evidence of the noise-enhanced stability and stochastic resonant activation in the prototype dynamical system, whose occurrence is maintained for different values of the delay feedback intensity.
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TL;DR: In this article, a stochastic reaction-diffusion-taxis model was used to analyze the picophytoplankton dynamics in the basin of the Mediterranean Sea, characterized by poorly mixed waters.
Abstract: In this paper, by using a stochastic reaction-diffusion-taxis model, we analyze the picophytoplankton dynamics in the basin of the Mediterranean Sea, characterized by poorly mixed waters. The model includes intraspecific competition of picophytoplankton for light and nutrients. The multiplicative noise sources present in the model account for random fluctuations of environmental variables. Phytoplankton distributions obtained from the model show a good agreement with experimental data sampled in two different sites of the Sicily Channel. The results could be extended to analyze data collected in different sites of the Mediterranean Sea and to devise predictive models for phytoplankton dynamics in oligotrophic waters.

68 citations

Journal ArticleDOI
TL;DR: In this paper, a hybrid energy harvester combining piezoelectric and electromagnetic transduction mechanisms is presented, which can be extensively applied in harvest vibration energy, and the mean harvested power is analyzed under additive and multiplicative Gaussian colored noise excitations.

38 citations

Journal ArticleDOI
TL;DR: A bifurcation analysis in a stochastic time-delayed birhythmic oscillator containing fractional derivative reveals that the rhythmic properties of the oscillator can be efficiently controlled by the fractional order damping.

31 citations

Journal ArticleDOI
TL;DR: In this paper, the authors provide a comprehensive review of state-of-the-art researches on the smooth and discontinuous (SD) oscillator with irrational nonlinearity, including fundamental dynamical characteristics of the unperturbed system, perturbed bifurcations, chaotic motions and also the coexistence of multiple atrractors.

12 citations

Journal ArticleDOI
TL;DR: In this paper , the authors provide a comprehensive review of state-of-the-art researches on the smooth and discontinuous (SD) oscillator with irrational nonlinearity, including fundamental dynamical characteristics of the unperturbed system, perturbed bifurcations, chaotic motions and also the coexistence of multiple atrractors.

12 citations

References
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Journal ArticleDOI
TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
Abstract: Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into consider­ably different states. Systems with bounded solutions are shown to possess bounded numerical solutions.

16,554 citations

Journal ArticleDOI
TL;DR: In this article, a particle which is caught in a potential hole and which, through the shuttling action of Brownian motion, can escape over a potential barrier yields a suitable model for elucidating the applicability of the transition state method for calculating the rate of chemical reactions.

7,289 citations

BookDOI
01 Jan 1983

7,182 citations

Journal ArticleDOI
TL;DR: In this paper, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry.
Abstract: The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally activated barrier crossing, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry. Theoretical as well as numerical approaches are discussed for single- and many-dimensional metastable systems (including fields) in gases and condensed phases. The role of many-dimensional transition-state theory is contrasted with Kramers' reaction-rate theory for moderate-to-strong friction; the authors emphasize the physical situation and the close connection between unimolecular rate theory and Kramers' work for weakly damped systems. The rate theory accounting for memory friction is presented, together with a unifying theoretical approach which covers the whole regime of weak-to-moderate-to-strong friction on the same basis (turnover theory). The peculiarities of noise-activated escape in a variety of physically different metastable potential configurations is elucidated in terms of the mean-first-passage-time technique. Moreover, the role and the complexity of escape in driven systems exhibiting possibly multiple, metastable stationary nonequilibrium states is identified. At lower temperatures, quantum tunneling effects start to dominate the rate mechanism. The early quantum approaches as well as the latest quantum versions of Kramers' theory are discussed, thereby providing a description of dissipative escape events at all temperatures. In addition, an attempt is made to discuss prominent experimental work as it relates to Kramers' reaction-rate theory and to indicate the most important areas for future research in theory and experiment.

5,180 citations

Book
19 Aug 1998
TL;DR: This chapter establishes the framework of random dynamical systems and introduces the concept of random attractors to analyze models with stochasticity or randomness.
Abstract: I. Random Dynamical Systems and Their Generators.- 1. Basic Definitions. Invariant Measures.- 2. Generation.- II. Multiplicative Ergodic Theory.- 3. The Multiplicative Ergodic Theorem in Euclidean Space.- 4. The Multiplicative Ergodic Theorem on Bundles and Manifolds.- 5. The MET for Related Linear and Affine RDS.- 6. RDS on Homogeneous Spaces of the General Linear Group.- III. Smooth Random Dynamical Systems.- 7. Invariant Manifolds.- 8. Normal Forms.- 9. Bifurcation Theory.- IV. Appendices.- Appendix A. Measurable Dynamical Systems.- A.1 Ergodic Theory.- A.2 Stochastic Processes and Dynamical Systems.- A.3 Stationary Processes.- A.4 Markov Processes.- Appendix B. Smooth Dynamical Systems.- B.1 Two-Parameter Flows on a Manifold.- B.4 Autonomous Case: Dynamical Systems.- B.5 Vector Fields and Flows on Manifolds.- References.

2,663 citations