Global chaos in a periodically forced, linear system with a dead-zone restoring force. (English) Zbl 1069.37027

Summary: The Poincaré mapping and the corresponding mapping sections for global motions in a linear system possessing a dead-zone restoring force are introduced through switching planes pertaining to two constraints. The global periodic motions based on the Poincaré mapping are determined, and the eigenvalue analysis for the stability and bifurcation of periodic motion is carried out. Global chaos in such a system is investigated numerically from the unstable global periodic motions analytically determined. The bifurcation scenario with varying parameters is presented. The mapping structures of periodic and chaotic motions are discussed. The Poincaré mapping sections for global chaos are given for illustration. The grazing phenomenon embedded in chaotic motion is observed in this investigation.


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