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**Application of multistage homotopy perturbation method to the chaotic Genesio system.**
*(English)*
Zbl 1246.65241

Summary: Finding accurate solution of chaotic system by using efficient existing numerical methods is very hard for its complex dynamical behaviors. In this paper, the multistage homotopy-perturbation method (MHPM) is applied to the chaotic Genesio system. The MHPM is a simple reliable modification based on an adaptation of the standard homotopy-perturbation method (HPM). The HPM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the chaotic Genesio system. Numerical comparisons between the MHPM and the classical fourth-order Runge-Kutta (RK4) solutions are made. The results reveal that the new technique is a promising tool for the nonlinear chaotic systems of ordinary differential equations.

### MSC:

65P20 | Numerical chaos |

37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |

37N35 | Dynamical systems in control |

### Keywords:

chaotic system; homotopy-perturbation method; algorithm; numerical comparisons; Runge-Kutta### References:

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