On the uniqueness of limit cycles in discontinuous Liénard-type systems

Abstract

In this paper, we investigate the uniqueness and stability of limit cycles for a nonlinear Liénard-type differential system with a discontinuity line. By employing a transformation technique and considering the characteristic exponent of periodic orbit, we give several criteria for the discontinuous planar nonlinear Liénard-type system. An example with different nonlinear functions $H(y)$ is presented to illustrate the obtained results.

Keywords

• discontinuity
• liénard-type system
• limit cycle
• uniqueness