A Modal Series Representation of Genesio Chaotic System

TL;DR

This paper introduces a novel analytic modal series method to represent and analyze the chaotic Genesio system, transforming nonlinear ODEs into a convergent series of linear equations for accurate solutions.

Contribution

It develops a new nonlinear modal series approach that converts chaotic nonlinear ODEs into linear series, enabling exact and efficient solutions.

Findings

The method accurately captures the chaotic behavior.

The series converges uniformly to the exact solution.

Simulation confirms high accuracy and efficiency.

Abstract

In this paper an analytic approach is devised to represent, and study the behavior of, nonlinear dynamic chaotic Genesio system using general nonlinear modal representation. In this approach, the original nonlinear ordinary differential equations (ODEs) of model transforms to a sequence of linear time- invariant ODEs. By solving the proposed linear ODEs sequence, the exact solution of the original nonlinear problem is determined in terms of uniformly convergent series. Also an efficient algorithm with low computational complexity and high accuracy is presented to find the approximate solution. Simulation results indicate the effectiveness of the proposed method.