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Shear-induced chaos

Kevin K Lin1 and Lai-Sang Young

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Recommended by R de la Llave

Guided by a geometric understanding developed in earlier works of Wang and Young, we carry out numerical studies of shear-induced chaos in several parallel but different situations. The settings considered include periodic kicking of limit cycles, random kicks at Poisson times and continuous-time driving by white noise. The forcing of a quasi-periodic model describing two coupled oscillators is also investigated. In all cases, positive Lyapunov exponents are found in suitable parameter ranges when the forcing is suitably directed.


PACS

05.45.Xt Synchronization; coupled oscillators

05.45.Pq Numerical simulations of chaotic systems

05.40.Ca Noise

MSC

65P20 Numerical chaos

60H40 White noise theory

37D45 Strange attractors, chaotic dynamics

37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)

37G15 Bifurcations of limit cycles and periodic orbits

Subjects

Statistical physics and nonlinear systems

Dates

Issue 5 (May 2008)

Received 29 May 2007, in final form 5 February 2008

Published 26 March 2008



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