The Coexisting Behaviors on the Boundary of a Duffing-like Oscillator with Signum Nonlinearity and Its FPGA-Based Implementation

Abstract

In this paper, the nonlinear behaviors of a Duffing-like system with signum function are investigated through the theory of discontinuous dynamical systems. The necessary and sufficient conditions for motion switchability on the boundary between two domains are analyzed 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. The effectiveness of the analysis conditions of periodic and chaotic motions with different mapping structures are verified through numerical simulations. Moreover, a hardware circuit of the Duffing-like system is established via Field Programmable Gate Array for the validation of the numerical analysis.