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On hyperjerky systems. (English) Zbl 1148.37026
Summary: Hyperjerky systems have been recently investigated by K. E. Clouverakis and J. C. Sprott [Chaos Solitons Fractals 28, No. 3, 739–746 (2006; Zbl 1106.37024)]. These authors have focused on the appearance of chaos in rather simple functional forms of such scalar, nonlinear ordinary differential equations of fourth order. We discuss the connection between externally driven nonlinear oscillators and specific uni- and bidirectionally coupled systems of two autonomous oscillators. This offers an interesting reinterpretation of simple chaotic forms of hyperjerky systems. We also provide some criteria that exclude chaotic behavior in some classes of hyperjerky systems.
MSC:
37D45Strange attractors, chaotic dynamics
34C28Complex behavior, chaotic systems (ODE)
37C10Vector fields, flows, ordinary differential equations
34C15Nonlinear oscillations, coupled oscillators (ODE)
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