A Duffing-Like Oscillator with Signum Nonlinearity

In this chapter, the nonlinear dynamics of a Duffing-like system with signum function are studied from the theory of discontinuous dynamical systems. The necessary and sufficient conditions for motion switchability on the boundary between two domains are presented to understand the switching mechanism. The switching velocity with varying different system parameters and the parameter mappings are carried out to illustrate the dynamical motions. The attraction basins are depicted to express the coexistence of the Duffing-like oscillator with different initial values, and the coexisting trajectories in phase-space with various initial conditions are also exhibited.