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

We prove a uniqueness result for limit cycles of the second order ODE x¨+x˙ϕ(x,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 [5] as a model of pedestrians' walk. This paper is an extension to equations with a non-linear g(x) of the results presented in [8].