On hyperjerky systems

Linz SJ

Abstract

Hyperjerky systems have been recently investigated by Clouverakis and Sprott [Chaos, Solitons & Fractals 28, (2006) 739.]. 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.