Showing papers in "International Journal of Nonlinear Sciences and Numerical Simulation in 2005"
TL;DR: In this article, a simple homotopy is constructed by the modified Lindstedt-Poincare method, by the solution and the coefficient of linear term are expanded into series of the embedding parameter.
Abstract: A simple homotopy is constructed, by the modified Lindstedt-Poincare method(He,J.H. International Journal of Non-Linear Mechanics , 37, 2002, 309-314 ), the solution and the coefficient of linear term are expanded into series of the embedding parameter. Only one iteration leads to accurate solution.
907 citations
TL;DR: In this paper, He's homotopy perturbation method is implemented to the model and the solution is obtained, the results reveal that the method is very effective and convenient.
Abstract: In this paper, He's Homotopy Perturbation Method is proposed for solving Volterra's Integro-differential Equation. The Volterra's population model is converted to a nonlinear ordinary differential equation and the solution of which is then approximated by using the differential transform method. He's homotopy perturbation method is implemented to the model and the solution is obtained. The results reveal that the method is very effective and convenient.
290 citations
252 citations
TL;DR: In this article, the authors improved the complex tanh-function method to find a traveling wave solution for equations with complex phases, which was then used to find the solutions of Hirota equation and the coupled Schrodinger-KdV equation.
Abstract: Recently, a number of methods for finding exact and numerical solutions of nonlinear partial differential equations were presented, such as the truncated Painleve expansion method[l], the Jacobi elliptic function expansion method[2-4], Adomian Pade approximation method[5] and F-expansion method [6-7] etc. The most efficient and straightforward methods to construct exact solutions of partial differential equations are the extended tanhfunction method [8, 9] and the complex tanhfunction method [10]. The purpose of this paper is to improve the complex tanh-function method to find travelling wave solution for equations with complex phases [10, 11], In Section 2, we introduce the improved complex tanh-function method. The improved complex tanh function method is then used to find the solutions of Hirota equation [12] in Section 3. In Section 4, this method is used to find the solution of the perturbed Wadati -Segur-Ablowitz equation [13]. The improved method is also applied to find travelling wave solution for the coupled Schrodinger -KdV equation [14, 15] in Section 5. Section 6 is devoted for conclusions.
136 citations
TL;DR: In this article, an adaptive control scheme for the synchronization of a unified chaotic system with an uncertain parameter is presented based on the Lyapunov stability theory, and the control performances are verified by numerical simulations.
Abstract: This paper addresses control for the synchronization of a unified chaotic systems with an uncertain parameter. It is noticed that this unified chaotic system contains the noted Lorenz, Lü, and Chen systems. Based on the Lyapunov stability theory, an adaptive control scheme for the synchronization has been presented. The control performances are verified by numerical simulations.
111 citations
TL;DR: The most probable number of elementary particles in the standard model is 69 particles as discussed by the authors, which is the largest known number of particles in any known particle model and is the smallest known number in the known universe.
Abstract: So far, we have already known experimentally 60 particles, but Mohamed Elnaschie's theory shows the most probable number of elementary particles in the standard model is 69 particles. Our journal shares a willingness to push big ideas forward while also asking how and how soon can Elnaschie's theory be tested experimentally. In the following pages, our journal offers an invited article by M.S. Elnaschie for World Year of Physics in 2005, and we hope that at least one hidden particle can be found in 2008. Ji-Huan He reports.
47 citations
TL;DR: In this paper, an idealized two-slit experiment is presented in which a hypothetical experimental set-up is constructed in such a way as to resemble a toy model giving information about the structure of quantum spacetime itself.
Abstract: In a sense Feynman's path integral and the transfmite sums over infinite dimensions used in the E-Infinity Cantorian spacetime theory are two complimentary ways of describing the outcome of the two slit experiment. In the present work an idealized two-slit experiment is envisaged in which a hypothetical experimental set-up is constructed in such a way as to resemble a toy model giving information about the structure of quantum spacetime itself. Thus starting from a very simple equation which may be interpreted as a physical realization of Gödel's undecidability theorem, we proceed to show that space-time is very likely to be akin to a fuzzy Kählerlike manifold on the quantum level. This remarkable manifold transforms gradually into a classical space-time as we decrease the resolution in a way reversibly analogous to the processes of recovering classical space-time from the Riemannian space of general relativity. The main message of the present paper is to emphasize that the two-slit experiment, as explained via Feynman's path integral, could be given a different interpretation by altering our classical concept of space-time geometry and topology. This would be in line with the development in theoretical physics since special and general relativity. In the final analysis it would seem that we have two different yet, from a positivistic philosophy viewpoint, completely equivalent alternatives to view quantum physics. Either we insist on what we see in our daily experiences, namely, a smooth four-dimensional space-time, and then accept, whether we like it or not, things such as probability waves and complex probabilities. Alternatively, we could see behind the charade of classical space-time the real far more elaborate and highly complex fuzzy space-time with infinite hierarchical dimensions as is the case with the so-called Fuzzy K3 or Ε-Infinity space-time. The reward for this imaginative picture is that we can return to real probabilities without a phase and an almost classical picture with the concept of a particle's path restored. We say almost classical because non-linear dynamics and deterministic chaos have long shown the central role of randomness in classical mechanics and that there can be no return to absolute determinism. This fact is reinforced once more in our model which is directly related not to Newtonian motion, but rather to a diffusion-like random walk similar to that used with great skill by Einstein and later on by Nagasawa and particularly the English-Canadian physicist Garnet Ord.
46 citations
TL;DR: In this article, a generalized Jacobi elliptic function expansion method is described and used for constructing many exact traveling wave solutions for nonlinear partial differential equations in a unified way, and applied this method to obtain many new Jacobi and Weierstrass double periodic elliptic functions solutions and multiple soliton solutions for (3+l)-dimensional Kadomtsev-Petviashvili (KP) equation as well as to the generalized Boussinesq equation.
Abstract: A new generalized Jacobi elliptic function expansion method is described and used for constructing many exact traveling wave solutions for nonlinear partial differential equations in a unified way. We apply this method to obtain many new Jacobi and Weierstrass double periodic elliptic function solutions and multiple soliton solutions for (3+l)-dimensional Kadomtsev-Petviashvili (KP) equation as well as to the generalized (2+l)-dimensional Boussinesq equation. This new generalized method can be applied to many other equations.
41 citations
TL;DR: For a large class of flows, the Navier-Stokes· equations based on the continuum approximation are adequate to model the fluid behavior as discussed by the authors, but for a variety of flows in which Knudsen number is of 0( 1), the continuum approximation is not valid.
Abstract: For a large class of flows, the Navier-Stokes· equations based on the continuum approximation are adequate to model the fluid behavior. However, for a variety of flows, in which Knudsen number is of 0( 1), the continuum approximation is not valid. The examples of such flows are the hypersonic flows about space vehicles in low earth orbit'' or flows in the channel of microelectromechanical (MEM) devices'. In both hypersonic flows with high altitude and flows in the microchannel, the Knudsen number, which is the ratio of the free path of molecules to the characteristic length of the flow, is high. So the higher-order extended or generalized hydrodynamic equations, derived from the Boltzmann equation, should be proposed to describe such flows. Burnett'' firstly developed a constitutive relationship for the stress and heat transfer terms by applying the Chapman-Enskog expansion to the collisional equilibrium and derived the original Burnett equations. Afterward Chapman and
34 citations
TL;DR: The three-dimensional universe of Newton ticks on without a hitch since two hundred years, the four dimensional space-time of Einstein's clock chimes hallelujah in unison for one hundred years and now suddenly the light of the new century of El-Naschie's Ε-infinity fractal space unfolds before us, which is in fact a sweeping generalization of what Einstein did in his general theory of relativity.
Abstract: The three-dimensional universe of Newton ticks on without a hitch since two hundred years, the four dimensional space-time of Einstein's clock chimes hallelujah in unison for one hundred years and now suddenly the light of the new century of El-Naschie's Ε-infinity fractal space unfolds before us, which is in fact a sweeping generalization of what Einstein did in his general theory of relativity. The genius of the three men is now forming a concerto which we will enjoy in this new century. Newton's universe is a God's eye view of the world; it looks the same to every observer, wherever he is and however he travels;
32 citations
TL;DR: In this paper, generalized variational principles for electrodynamic inner problem are obtained by Lagrange multiplier method, which is used to solve the inner problem of electrodynamics.
Abstract: Generalized variational principles for electrodynamic inner problem are obtained by Lagrange multiplier method.
TL;DR: In this paper, a bi-linear hysteresis model is proposed to describe the nonlinear response of an electromagnetic activated magneto-rheological fluid (MRF) damper.
Abstract: In this paper, a bi-linear hysteresis model is proposed to describe the nonlinear response of an electromagnetic activated magneto-rheological fluid (MRF) damper. The model parameters have significant effects on MRF damper. An analytical solution for the primary resonance of an SDOF system with skyhook damping is obtained. There exists a specific condition for the primary resonance for discussed system.
TL;DR: In this article, a time delay feedback controlling method is applied to the system and the effects of the change of parameters in the system can be found in the bifurcation diagrams and parametric diagrams.
Abstract: A time delay Duffing system is studied in this paper. This system is forced by harmonically periodic vibration to enrich dynamics behaviors. Because of the nonlinear terms of the system, the system exhibits both regular and chaotic motions. By using Lyapunov direct method, the stability of the controlled system can be determined. And by applying various numerical results, such as phase portraits, Poincare maps, time history and power spectrum analysis, the behaviors of the periodic and chaotic motion are presented. The effects of the change of parameters in the system can be found in the bifurcation diagrams and parametric diagrams. Finally, a time delay feedback controlling method is applied to the system. It is found that the controller can effectively control the chaotic orbits to the regular ones.
TL;DR: In this paper, a three-dimensional model is presented for the quantitative prediction of skin injury resulting from certain thermal exposure on the surface, which is based on the skin damage equation proposed by Henriques and Moritz for the process of protein denaturation.
Abstract: A three-dimensional model is presented for the quantitative prediction of skin injury resulting from certain thermal exposure on the surface. The model is based on the skin damage equation proposed by Henriques and Moritz for the process of protein denaturation. Different from the standard Arrhenius model for protein damage rate, in which the activation energy includes chemical reaction only, strain energy of tissue due to thermal stress is also considered in the current model. Skin thermal response is modeled using the bioheat transfer equation by including water diffusion on the skin surface, and the corresponding thermal stress is predicted using the modified Duhamel-Neuman equation. Strain energy is then obtained by the stress-strain relation. The extent of burn injury is computed from the transient temperature solution and the effect of strain energy on skin damage is investigated. The time-dependent partial differential equations (PDEs) are discretized using Crank-Nicholson finite difference scheme and the resulting sparse linear systems are solved iteratively.
TL;DR: In this paper, a relationship between the radius of the jet and the axial distance from the nozzle, and a scaling relation between fiber radius and the AC frequency are obtained. But the relationship between fiber diameter and the frequency is not defined.
Abstract: The application of AC potential to electrospinning results in a significant reduction in the amount of fiber ‘whipping’, so that fiber radius can be easily controlled. A relationship between the radius of the jet and the axial distance from nozzle, and a scaling relation between fiber radius and the AC frequency are obtained.
TL;DR: In this paper, a perturbation-incremental scheme was proposed and extended to overcome the disadvantage of CMT for delay-induced non-resonant double Hopf bifurcations.
Abstract: This paper deals with delay-induced non-resonant double Hopf bifurcations, chaos and quantitative computation of the bifurcating solutions derived from the bifurcations in van der Pol-Duffing system with delayed feedback. The sufficient and necessary condition of 1:1.414 double Hopf bifurcation occurring in the system is obtained by linear analysis and Hopf bifurcation theorem when the time delay and feedback gain are regarded as bifurcation parameters. The center manifold theorem (CMT) and method of normal forms are employed to reduce the system to be 4-dimensional center manifold and to classify dynamics in the neighborhood of the bifurcation point. For values of the time delay and feedback close to the point, the approximate expressions provided by CMT are given quantitatively to represent those harmonic solutions in the neighborhood of the bifurcation point. CMT is invalid quantitatively for those values far away from the bifurcation point. A perturbation-incremental scheme (PIS) is proposed and extended to overcome the disadvantage of CMT. The numerical simulation is used, both qualitatively and quantitatively, to verify the analyzed results, including the periodic and quasi-periodic solutions. The results show that PIS is efficient. PIS together with CMT may provide both the qualitative and quantitative analyses for delayed systems. This paper also shows that there are rich dynamical behaviors in the system under consideration, such as "amplitude death", periodic and quasi-periodic motions, and chaos. These results have some potential applications in, for example, vibration control, synchronization, producing complex dynamics for some specific goals and so on.
TL;DR: In this paper, the phase synchronization of two coupled Morris-Lecar neurons was investigated and the critical value was determined as a function of the conditional Lyapunov exponents of the synchronization manifold, the mean synchronization error and the maximum synchronization error.
Abstract: A single Morris-Lecar neuron model can produce a variety of spontaneous firing rhythm patterns, such as spiking and bursting activities, by adjustment of the equilibrium potential of potassium channel. In the two electrically coupled identical Morris-Lecar neurons, it is shown that the increase of the coupling strength induces complete synchronization. The critical value is determined as a function of the conditional Lyapunov exponents of the synchronization manifold, the mean synchronization error and the maximum synchronization error. Based on a well-defined phase function, phase synchronization of two coupled Morris-Lecar neurons is further studied.
TL;DR: In this article, the authors argue that an effective approach to the high-energy regime of QFT demands the tools of complex dynamics and fractal operators, and the unexpected consequences of using fractal operator to model complexity beyond the current range of quantum field theory are outlined and discussed.
Abstract: The standard model embodies our current knowledge of elementary particle physics and represents a welltested framework for the study of non-gravitational phenomena at low energies. It is built on the foundations of relativistic quantum field theory (QFT), which provides the correct description of electroweak and strong interactions involving leptons and quarks. It is generally believed that, extending the validity of QFT to energies on or beyond the TeV range must include the unavoidable signature of vacuum fluctuations and strong-field gravity. We argue that an effective approach to the high-energy regime of QFT demands the tools of complex dynamics and fractal operators. The unexpected consequences of using fractal operators to model complexity beyond the current range of QFT are outlined and discussed.
TL;DR: In this article, the bifurcation phenomena of a generalized Camassa-Holm equation have been investigated and the influence of the singular line on the properties of the equilibrium points has been explored and the transition boundaries are obtained to divide the parameter space into different regions.
Abstract: The bifurcation phenomena of a generalized Camassa-Holm equation have been investigated in this paper. It is noted that there exists a singular line on the topological vector field. The influence of the singular line on the properties of the equilibrium points has been explored and the transition boundaries are obtained to divide the parameter space into different regions. In each region, different types of phase trajectories associated with different traveling wave solutions can be observed, and accordingly, the existence conditions for different traveling wave solutions can be established.
TL;DR: In this article, the cosmological consequences of such extension appear relevant, since thanks to the Fantappie group, the model of the Big Bang and that of stationary state become compatible, in particular if we abandon the idea of the existence of only one time gauge, since we do not see the whole Universe but only a projection.
Abstract: In this paper starting from the Fantappie group we will consider its properties in connection with E-infinity Cantorian space-time. The cosmological consequences of such extension appear relevant, since thanks to the Fantappie group, the model of the Big Bang and that of stationary state become compatible. In particular, if we abandon the idea of the existence of only one time gauge, since we do not see the whole Universe but only a projection, the two models become compatible. In the end we will see the effects of the projective fractal geometry also on the galactic and extra-galactic dynamics; in particular, we analyze the effects of Fantappie's transformation on gravitational lenses and we will see that the gravitational lensing effects could be a good tool to verify this theory.
TL;DR: In this article, a new adaptive synchronization principle is proposed to resolve the chaos synchronization of the drive-driven type chaotic systems, where an adaptive response system is designed to synchronize with a given chaotic drive system whose dynamical model is subjected to disturbances and/or some unknown parameters.
Abstract: In this paper, we propose a new adaptive synchronization principle to resolve the chaos synchronization of the drive-driven type chaotic systems. An adaptive response system is designed to synchronize with a given chaotic drive system whose dynamical model is subjected to disturbances and/or some unknown parameters. To guarantee the synchronization between the coupled chaotic oscillators, proper coupling constants are selected by the Lyapunov stability theory and Hurwitz Theorem. Two well-known chaotic systems: Lorenz system and Chua's circuit are considered as illustrative examples to demonstrate the effectiveness of the proposed scheme.
TL;DR: In this paper, the effect of damage on the nonlinear dynamic behaviors of damaged viscoelastic thin plates with a transverse periodic excitation is investigated based on the Von Kärmän plate theory and Boltzmann superposition principle.
Abstract: In this paper, the effect of damage on the nonlinear dynamic behaviors of damaged viscoelastic thin plates with a transverse periodic excitation is investigated. Based on the Von Kärmän plate theory and Boltzmann superposition principle, the nonlinear equations of motion for the viscoelastic plate with damage are derived and expressed in the term of the mid-plane displacement. The effects of the damage value and damage position on the bifurcation and chaos of the plates are discussed numerically. Present research results provide a theoretical basis for the design of dynamic stability and nondestructive testing of structures.
TL;DR: Application of fractal analysis may provide new approaches to monitoring the normal aging process as well as to assessing cardiac risk in a 55-year-old man.
Abstract: Daily heart rate variability has been shown to be fractal and can be characterized by the Hurstcoefficient (Η). Η is < 0.5 for anti-correlated time-series, > 0.5 for positively correlated series, and = 0.5 for random white noise. Heart rate and diastolic and systolic blood pressure were measured every morning for 512 days in a 55-year-old man. The dispersional analysis method was applied by calculating the standard deviation (SD) of the each signal at a grouped interval of Ν = 2, 4, 8, 16, 32, 64, 128, 256 and 512. There was a power-law relation between SD and N. From the exponent, Η was derived. Η was 0.75 for systolic, 0.71 for diastolic blood pressure and 0.69 for heart rate variation, respectively. Application of fractal analysis may provide new approaches to monitoring the normal aging process as well as to assessing cardiac risk.
TL;DR: In this article, an adaptive control scheme based on the Lyapunov stability theory was presented for the synchronization of two four dimensional chaotic systems with uncertain parameters by nonlinear control laws.
Abstract: This work presents adaptive synchronization between two four dimensional chaotic systems with uncertain parameters by nonlinear control laws. Based on the Lyapunov stability theory, an adaptive control scheme for the synchronization has been presented. The control performances are verified by a numerical simulation.
TL;DR: In this article, a variational method is applied to a unidirectionally coupled single-mode optical system for the general characteristics of aperiodic stochastic resonance (ASR) and stochastically synchronization in the linear response background, and it is shown that ASR in the low frequency domain exists in all stable cases by means of coherence function.
Abstract: The variational method is applied to a unidirectionally coupled single-mode optical system for the general characteristics of aperiodic stochastic resonance (ASR) and stochastic synchronization in the linear response background. It is shown that ASR in the low-frequency domain exists in all stable cases by means of coherence function, but the stochastic synchronization in the weak noise level exists only when the drive subsystem is bistable or multistable. However, the curve of correlation coefficient vs. the noise intensity exhibits ASR-like behavior only when the drive subsystem is monostable. The relaxation property of the drive subsystem is found to be responsible for these different characteristics.
TL;DR: It is obtained that the genesis of the integer multiple firing is the response of the corresponding deterministic system to the weak random pulses of Gaussian white noise, and the integers fired are the stochastic "fold/homoclinic" bursting with one spike per burst in essence.
Abstract: Integer multiple firing due to Gaussian white noise is studied in the stochastic Chay neuronal model. It is obtained that the genesis of the integer multiple firing is the response of the corresponding deterministic system to the weak random pulses of Gauss ian whi te noise, and the integer multiple firing is the stochastic \"fold/homoclinic\" bursting with one spike per burst in essence.
TL;DR: By applying the techniques of active control, this investigation demonstrates that the time evolution of the slave system can be synchronized by the master system, even though these two systems are strictly different.
Abstract: This paper addresses the synchronization of two chaotic systems with different order. By applying the techniques of active control, this investigation demonstrates that the time evolution of the slave system can be synchronized by the master system, even though these two systems are strictly different. Two examples are given to demonstrate the techniques. In the first example, Duffing oscillator (second order) is selected as the slave system and Rössler (third order) system as the master system. In the second example, Lorenz system (third order) is synchronized by two-level laser system (fifth order). Furthermore, the mean squared error (MSE) of two synchronized systems is discussed, and the method is analyzed further.
TL;DR: In this paper, a predator-prey meta-population model with delay is investigated, where a collection of prey sub-populations live in two identical patches with a constant probability per unit time for individual prey in a patch migrating to another patch.
Abstract: A predator-prey meta-population model with delay is investigated. A collection of prey sub-populations lives in two identical patches with a constant probability per unit t ime for individual prey in a patch migrating to another patch. Due to broad-scale foraging behavior or long-range juvenile dispersal, predators are assumed to be homogeneously distributed over these patches. The stability and bifurcation analysis for this model is made. It is shown that the delay has an effect on stability switching of the positive equilibrium solution, and population cycles appear under the Hopf and Hopf-Hopf bifurcations.