On periodic solutions of Rayleigh equation

Abstract

New sufficient conditions for the existence and uniqueness of a periodic solution of a system of differential equations equivalent to the Rayleigh equation are obtained. In contrast to the known results, the existence proof of at least one limit cycle of the system is based on applying curves of the topographic Poincare system. The uniqueness of the limit cycle surrounding a complex unstable focus is proved by the Otrokov method.

Keywords

• poincare
• rayleigh equation
• van der pol equation
• limit cycle
• existence
• uniqueness