KEHUI SUN*,†,‡ and J. C. SPROTT†,§
*School of Physics Science and Technology,
Central South University, Changsha 410083, China
Department of Physics,
University of Wisconsin Madison, WI 53706, USA

Received July 10, 2009; Revised August 3, 2009


A sinusoidally-driven system with a simple signum nonlinearity term is investigated through an analytical analysis as well as dynamic simulation. To obtain the correct Lyapunov exponents, the signum function is replaced by a sharply varying continuous hyperbolic tangent function. By phase portraits, Poincar´e sections and bifurcation diagrams, the rich dynamic behaviors of this system are demonstrated, such as an onion-like strange attractor, pitchfork and attractor merging bifurcations, period-doubling routes to chaos, and chaotic transients in the case of small damping. Moreover, the chaos persists as the damping is reduced to zero.

Ref: K. Sun and  J. C. Sprott, International Journal of Bifurcation and Chaos 20, 1499-1507 (2010)

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