Homotopy approach for the hyperchaotic Chen system

In this paper, the numerical–analytical solution for the hyperchaotic Chen system is obtained via the multistage homotopy analysis method (MSHAM). An analytical form of the solution within each time interval is given, which is not possible using standard numerical methods. The numerical results obtained by the MSHAM and the classical fourth-order Runge–Kutta (RK4) method are in complete agreement. Moreover, the residual error for the MSHAM solution is given for each time interval.

[1]  S. Liao.  Notes on the homotopy analysis method: Some definitions and theorems , 2009 .

[2]  S. Liao,et al.  Beyond Perturbation: Introduction to the Homotopy Analysis Method , 2003 .

[3]  Pei Yu,et al.  Hyperchaos synchronization and control on a new hyperchaotic attractor , 2008 .

[4]  Mohd. Salmi Md. Noorani,et al.  On accuracy of Adomian decomposition method for hyperchaotic Rössler system , 2009 .

[5]  R. Nazar,et al.  Solutions of Heat-Like and Wave-Like Equations with Variable Coefficients by Means of the Homotopy Analysis Method , 2008 .

[6]  Ju H. Park.  Adaptive synchronization of hyperchaotic Chen system with uncertain parameters , 2005 .

[7]  Mohd. Salmi Md. Noorani,et al.  Adaptation of homotopy analysis method for the numeric–analytic solution of Chen system , 2009 .

[8]  Mohd. Salmi Md. Noorani,et al.  NUMERICAL EXPERIMENTS ON THE HYPERCHAOTIC CHEN SYSTEM BY THE ADOMIAN DECOMPOSITION METHOD , 2008 .

[9]  T. Hayat,et al.  Homotopy Solutions for a Generalized Second-Grade Fluid Past a Porous Plate , 2005 .

[10]  S. Abbasbandy.  The application of homotopy analysis method to solve a generalized Hirota–Satsuma coupled KdV equation , 2007 .

[11]  Zhi Zong,et al.  Generalizing homotopy analysis method to solve Lotka-Volterra equation , 2008, Comput. Math. Appl..

[12]  S. Abbasbandy,et al.  Homotopy analysis method for quadratic Riccati differential equation , 2008 .

[13]  Zhenya Yan,et al.  Controlling hyperchaos in the new hyperchaotic Chen system , 2005, Appl. Math. Comput..

[14]  Guanrong Chen,et al.  Generating Hyperchaos via State Feedback Control , 2005, Int. J. Bifurc. Chaos.

[15]  R. Nazar,et al.  On the homotopy analysis method for the exact solutions of Helmholtz equation , 2009 .

[16]  Mohd. Salmi Md. Noorani,et al.  Application of the differential transformation method for the solution of the hyperchaotic Rössler system , 2009 .

[17]  Shaher Momani,et al.  A reliable algorithm of homotopy analysis method for solving nonlinear fractional differential equations , 2010 .

[18]  Ishak Hashim,et al.  Approximate analytical solutions of systems of PDEs by homotopy analysis method , 2008, Comput. Math. Appl..

[19]  T. Hayat,et al.  On analytic solution for thin film flow of a fourth grade fluid down a vertical cylinder , 2007 .

[20]  T. Hayat,et al.  MHD rotating flow of a viscous fluid over a shrinking surface , 2007 .