Chaos. Mirons & Frocrals Vol 4. No. 2. pp. 201-211, 1994 Copyright 0 1994 El&m Scmm Ltd Prmted in Great Britain. All riehfs resewed 096%0779/9;$6.00 + .oo Synchronous Chaotic Behaviour of a Response Oscillator with Chaotic Driving NIKOLAI F. RUL’KOV and ALEXANDER R. VOLKOVSKII Radiophysical Department, Lobachevskii State University, 23 Gagarin Avenue, 603600-Nizhny Novgorod, Russia and ANGEL RODRIGUEZ-LOZANO, EZEQUIEL DEL RIO and MANUEL G. VELARDE Instituto Pluridisciplinar, Universidad Complutense, Paseo Juan XXIII, No. 1, 28040-Madrid, Spain zyxwvutsrqponm (Received 20 May 1993 and in revised form 8 August 1993) Abstract -Synchronization of chaotic self-excited oscillations and chaotic synchronous response are studied using chaotic electronic oscillators with unidirectional coupling. 1. INTRODUCTION The phenomenon of synchronization of self-excited oscillators with chaotic behaviour has a high potential for applications in electronics, physics, biology and other fields. This phenomenon has been observed in studies of chaotic oscillators with mutual and unidirec- tional coupling, see for example [l-lo]. In recent papers [ll-131, stable regimes of synchronous chaotic response caused by chaotic driving were also demonstrated in several examples. Attempts to understand the nature of the synchronization and the response, common features and differences of these phenomena comes from analogy with a classical problem of periodic synchronization and response in the van-der-Pol oscillator driven with an external force X - p(A - x2).t + 3x = nsinwor (1) where the parameters q, p and Iw - 0~1 are positive and much smaller than unity. If the parameter A has positive values, then equation (1) describes the phenomenon of forced synchronization of self-excited periodic oscillations. If A has negative value, then equation (1) describes the resonant response of the oscillator with nonlinear damping. Although this analysis refers to small parameter values, the nonlinear phenomena studied on the basis of this example have universal value to lead to understanding nonlinear behaviour in a large class of oscillatory systems. In this paper we provide some new results when driving and response systems are described by the following equation j;-’ + A32 + A2i + A,x + A&x) = 0. (2) Communicated by G. Nicolis. 201