Coexistence, bifurcation and chaos of a periodically forced duffing system with absolute nonlinearity

In this paper, the nonlinear dynamics of a Duffing nonautonomous oscillator with absolute function is investigated, and the switching boundary and the corresponding domains are shown. Based on the discontinuous dynamical theory, the motions of the non-smooth duffing system at the switching boundary are studied, and the corresponding analysis conditions of the different motions are obtained, and the parameter mappings are also given. Through numerical simulations, chaotic motions and period orbits are described in detail with different parameters and initial conditions, and the switching bifurcation diagrams through the boundary and basins of attractors are also drawn to investigate the behaviors of the system and coexistence of different attractors.