We prove a uniqueness result for limit cycles of the second order ODE x''+f(x,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].
Existence and uniqueness of limit cycles in a class of second order ODE's with inseparable mixed terms
Sabatini, Marco
2010-01-01
Abstract
We prove a uniqueness result for limit cycles of the second order ODE x''+f(x,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].File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione