On necessary and sufficient conditions for chaos to occur in Duffing's equation: an Heuristic approach

Many different explanations have been offered for the occurrence of chaos in Duffing's equation. Holmes has derived a criterion for the onset of chaos using Melnikov theory that is based upon the initial entanglement of the unstable manifold with the stable limit cycle. Moon offered a criterion based on physical principles by considering how much energy a trajectory had to possess to get out of the potential well of one of the stable limit cycles. In this paper, conclusive numerical evidence is offered that in order for steady state chaos to occur in this system, there must be a near intersection of the stable and unstable steady state limit cycles in the phase space of Duffing's equation. © 1988 Academic Press Limited.

Duke Scholars

Author Earl H. Dowell Thomas Lord Department of Mechanical Engineering and Materia ...