Simplest Driven Conservative Chaotic Oscillator

H. P. W. Gottlieb
School of Science, Griffith University, Nathan, Queensland 4111, Australia

J. C. Sprott
Department of Physics, University of Wisconsin, Madison, WI 53706, USA

(Received 21 August 2001: received in revised form 2 November 2001; accepted 2 November 2001)

ABSTRACT

Sinusoidally driven oscillator equations with a power-law nonlinearity are investigated computationally to determine the driving frequency which produces the "most chaos", i.e., the maximixed largest Lyapunov exponent.  It is argued that the "simplest" such driven chaotic oscillator has a cubic nonlinearity x3.

Ref: H. P. W. Gottlieb and J. C. Sprott, Phys. Lett. A 291, 385-388 (2001)

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Fig. 1. Largest Lyapunov exponent lambda versus driving angular frequency omega for Eq. (1) with p=3.
[Figure 1]

Fig. 2. Poincaré section in the x-dx/dt plane for p=3, omega=1.88 case of Eq. (1), for omega t mod 2pi=0.
[Figure 2]

Fig. 3. As for Fig. 1, but with p=5.
[Figure 3]

Fig. 4. Largest positive Lyapunov exponent for arbitrary p and  in Eq. (1), shown on a grey scale--blacker
tone for larger exponent.