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Numerical versus analytical conditions for chaos, using the example of the Duffing oscillator. (English) Zbl 1160.65350

Summary: A numerical technique (based on solving a boundary value problem) is used to trace a route to chaos via period doubling, and to obtain the parameter set of sudden transition to chaos. Results are compared with those found by approximate analytical methods.

MSC:

65P20 Numerical chaos
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C28 Complex behavior and chaotic systems of ordinary differential equations
70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
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