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:
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