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, Poincaré 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.
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Sun et al. (2010) studied this question.
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