Chaos and hyperchaos in coupled Kerr oscillators

We analyze numerically some aspects of the chaotical dynamics of two mutually coupled Kerr anharmonic oscillators. Both oscillators are damped and driven by external time-dependent forces. The coupling between the oscillators is a critical parameter which governs the existence of chaos. If the oscillators are uncoupled one behaves chaotically whereas the other remains nonchaotic. The coupled system exhibits not only chaotic but also nonchaotic or even hyperchaotic behavior according to the magnitude of coupling. To indicate chaotic behavior of the system we make use of the spectrum of Lyapunov exponents. The topology of the motion is visualized on the appropriate phase portraits. (C) 2000 Published by Elsevier Science B.V. All rights reserved.