2007•Journal of Hengyang Normal UniversityRequires access

Studies of Chaotic Dynamics of A Duffing Oscillator

Wang Yan-qun

Abstract

This paper studies the chaotic dynamics of a Duffing oscillator.By using the direct perturbation method,we construct the general solution of the 1st-order equation.Theoretical analysis reveals that the boundedness condition of the general solution contains the Melnikov chaotic criterion.When the system cannot meet the perturbation conditions,numerical simulations show that,whith the increase in the amplitude of the external forcing,the system undergoes a process from period doubling to chaos.We also find that the chaos of the system canbe effectively suppressed by adjusting some parameters.

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Key concepts: Duffing equation, Chaotic, Perturbation (astronomy), Amplitude, Mathematics, Forcing (mathematics), Control theory (sociology), CHAOS (operating system)