Existence and uniqueness of limit cycles in a class of second order ODE's with inseparable mixed terms

Abstract

We prove a uniqueness result for limit cycles of the second order ODE $\ddot{x}+\dot{x}\varphi (x,\dot{x})+g(x)=0$. Under mild additional conditions, we show that such a limit cycle attracts every non-constant solution. As a special case, we prove limit cycle's uniqueness for an ODE studied in \cite{ETA} as a model of pedestrians' walk. This paper is an extension to equations with a non-linear $g(x)$ of the results presented in \cite{S}.

References in corpus (2)

• Existence and uniqueness of limit cycles in a class of second order ODE's with inseparable mixed terms
• Existence and uniqueness of limit cycles in a class of second order ODE's

Cited by in corpus (2)

• Existence and uniqueness of limit cycles in a class of second order ODE's with inseparable mixed terms
• On the uniqueness of limit cycles for Liénard equation: the legacy of G. Sansone