Regular and Chaotic Behaviors of Modified Rayleigh Duffing oscillator

TL;DR

This paper investigates the complex dynamics of a modified Rayleigh-Duffing oscillator, analyzing how system parameters influence bifurcations, chaos, and hysteresis through analytical and numerical methods.

Contribution

It introduces a detailed analysis of the bifurcation and chaotic behavior of the modified Rayleigh-Duffing oscillator, highlighting the effects of parameter variations on system dynamics.

Findings

Identification of bifurcation structures and chaos

Observation of hysteresis and jump phenomena

Correlation between Lyapunov exponents and basin attractions

Abstract

The regular and chaotic behavior of modified Rayleigh-Duffing oscillator is studied. We consider in this paper the dynamics of Modified Rayleigh Duffing oscillator. The harmonic balance method are used to find the amplitudes of the oscillatory states, and analyze. The influence of system parameters are clearly found on the bifurcations in the response of this system is investigated. It is found also hysteresis and jump phenomenon are appered or desappered when certain parameters incrases or descrases. Various bifurcation structures, the variation of the Lyapunov exponent are obtained, using numerical simulations of the equations of motion. Various basin attraction are used to confirm the predictions of bifurcation structures and its corresponds Lyapunov exponent.