The analytical predictive criteria for chaos and escape in nonlinear oscillators: A survey

The purpose of this paper is to provide a brief summary of the various analytical predictive criteria in order for “strange phenomena” to occur in a class of softening nonlinear oscillators, oscillators which may exhibit escape from a potential well. Implications of Melnikov's criteria are discussed first and transient chaos in the twin-well potential oscillator is illustrated. Three different heuristic criteria for steady state chaos or escape solution, proposes by F. Moon, G. Schmidt and W. Szemplińskia-Stupnicka, are then presented and compared to computer simulation results.

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