From Limit Cycles to Strange Attractors
نویسندگان
چکیده
منابع مشابه
From Limit Cycles to Strange Attractors
We define a quantitative notion of shear for limit cycles of flows. We prove that strange attractors and SRB measures emerge when systems exhibiting limit cycles with sufficient shear are subjected to periodic pulsatile drives. The strange attractors possess a number of precisely-defined dynamical properties that together imply chaos that is both sustained in time and physically observable.
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Guided by a geometric understanding developed in earlier works of Wang and Young, we carry out some numerical studies of shear-induced chaos. 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, posit...
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We prove the emergence of chaotic behavior in the form of horseshoes and strange attractors with SRB measures when certain simple dynamical systems are kicked at periodic time intervals. The settings considered include limit cycles and stationary points undergoing Hopf bifurcations. This paper is about a mechanism for producing chaos. The scheme consists of periodic kicks interspersed with long...
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We consider parametrized families of diieomorphisms bifurcating through the creation of critical saddle-node cycles and we show that they exhibit H enon-like strange attractors for a set of parameter values which has positive Lebesgue density at the bifurcation value. This is the rst example of a bifurcation mechanism displaying such prevalence of H enon-like chaotic behaviour. Furthermore, for...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2010
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-010-0994-y