A new method of detection of chaos in dynamical systems generated by time-periodic nonautonomous differential equations is presented. It is based on the existence of some sets (called periodic isolating segments) in the extended phase space, satisfying some topological conditions. By chaos we mean the existence of a compact invariant set such that the Poincare map is semiconjugated to the shift on two symbols and the counterimage (by the semiconjugacy) of any periodic point in the shift contains a periodic point of the Poincare map. As an application we prove that the planar equation z* =(1+e i,t |z| 2 ) zÄ generates chaotic dynamics provided 0<, 1Â288.1997 Academic Press

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An extension of the recently introduced Srzednicki Wo jcik method for detecting chaotic dynamics in periodically forced ordinary differential equations is presented. As an application of the method we construct a topological model for the planar equationand we show by a continuation argument that the symbolic dynamics on three symbols for the topological model continues to Eq. (1) for 0<} 0.495. 2000Academic Press