Discontinuous Dynamic Analysis of a Modified Duffing-Rayleigh System With a Piecewise Quadratic Function

The discontinuous dynamical behavior of a modified Duffing-Rayleigh system with a piecewise quadratic function is studied. The necessary and sufficient conditions for motion switchability at the velocity boundary are investigated through the theory of discontinuous dynamical systems. Various motions through the boundary are demonstrated by the parameter maps and coexisting bifurcation diagrams. The coexistence of an example system under different initial conditions is illustrated by attraction basins, and the trajectories in phase plane. The periodic and chaotic motions with different mapping structures are analyzed for a better understanding of the motion switching mechanism. Through Multisim, the circuit experiment proves the effectiveness of the theoretical analysis.