Sha Wang

Application of multistage homotopy-perturbation method in hybrid synchronization of chaotic systems

In this paper, the multistage homotopy-perturbation method (HPM) is applied to realize the synchronization between the Lorenz system and the Chen system using active control. The multistage HPM is only a simple modification of the standard HPM, in which it is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions. The simulation results reveal that the multistage method is an effective tool to give the approximate analytical solutions for chaotic systems.

Bifurcation analysis of a two-dimensional simplified Hodgkin–Huxley model exposed to external electric fields

In this paper, the dynamical behaviors of a two-dimensional simplified Hodgkin–Huxley (H–H) model exposed to external electric fields are investigated through qualitative analysis and numerical simulation. A necessary and sufficient condition is proposed for the existence of the Hopf bifurcation. Saddle-node bifurcations and canards of the simplified model with the coefficients of different linear forms are also discussed. Finally, the bifurcation curves with the coefficients of different linear forms are shown. The numerical results demonstrate that some linear forms can retain the bifurcation characteristics of the original model, which is of great use to simplify the H–H model for the real-world applications.

Hybrid Lag Function Projective Synchronization of Discrete Chaotic Systems with Different Orders

This paper presents a novel method to achieve hybrid lag function projective synchronization between two different discrete chaotic systems with different orders, which (is a further development of generalized function projective synchronization. On the basis of Lyapunov stability theory, a controller is designed to guarantee synchronization of drive and response systems. Numerical simulations are provided to verify the proposed synchronization approach.

Three Improved Euler Methods for a Class of Simplified Quasi-cubics Function

The simplified quasi-cubics function is used quite common in the ordinary differential equation, which is used to describe the biological neuron model. As complexity of the biological neuron model, its analytical solution hardly can be solved in common situation. Numerical solution of the model is very important in reality. Three fast convergence methods are proposed for the simplified function by means of changing the step size of the classical Euler method in this manuscript. The results obtained are pretty good. First method is to correct the step size of two directions. Second method is to correct and encrypt two directions step size. And the last method is to search unidirectional step size. On one hand, the feasibility of the three methods are proved based on the theoretical analysis. On the other hand, numerical results and comparison show that the advised three methods are effective to get the numerical solution with small population size, enhanced convergence speedup and improved precision.

Bifurcation analysis of a two-dimensional simplified hodgkin-huxley model exposed to external electric fields

This paper studies the dynamical behaviors of a two-dimensi- onal simplified Hodgkin-Huxley (H-H) model exposed to external electric fields through qualitative analysis and numerical simulation. A necessary and sufficient condition is proposed for the existence of the Hopf bifurcation. Other type of bifurcations of the simplified model with the coefficients of different linear forms are also discussed. Finally, the bifurcation curves with the coefficients of different linear forms are shown. The numerical results demonstrate that some linear forms can retain the bifurcation characteristics of the original model, which is of great use to simplify the H-H model for real-world applications.

Function Projective Synchronization of Chaotic Fractional Order Systems with Different Dimensions

The function projective synchronization of different dimensional fractional order chaotic systems is investigated in this letter. According to the stability theorem of linear fractional order systems, a nonlinear controller to realize the synchronization is obtained. The function projective synchronization between the fractional order chaotic and hyperchaotic Rossler systems is successfully achieved to show the feasibility of the proposed method.

The Hybrid Function Projective Synchronization of Discrete Chaotic Systems

Generalized projective synchronization is further studied. Based on the Lyapunov stability theory, a new kind of synchronization scheme is presented to achieve function projective synchronization between two different discrete chaotic systems. The involved numerical simulations are given to show the feasibility of theoretical results obtained.