Stability and chaos for an adjustable excited oscillator with system switch

Abstract

A linear spring-damper dynamic oscillator with excitations is studied in the paper, and a set of subsystems are defined by adjusting the constant and magnitude of the periodic external forces. A triangular domain is defined in the phase plane coordinate system, and such a dynamic system will switch to the corresponding subsystem when the flow arrives at the boundary or corner for such a domain. Through employing the theory of discontinuous, the vector fields for the subsystems have been determined which is the necessary conditions of motion ‘bouncing’ within such a triangular domain. To describe the periodic motions of such an oscillator, the generic mappings are constructed. The periodicity and stability for the motion in the steady-state have been discussed. Analytical and numerical predictions have been carried out through phase plane and switching sections to illustrate the effectiveness of the design of the subsystems under the proposed switching scheme. Periodic and chaotic motions have been simulated to institutively illustrate the system switch and stability for such a spring-damper oscillator with adjustable excitations.