The problem is studied of chaotic behaviour of a time dependent perturbation of a discontinuous differential equation whose unperturbed part has a sliding homoclinic orbit that is a solution homoclinic to a hyperbolic fixed point with a part belonging to a discontinuity surface. It is assumed that the time dependent perturbation satisfies a kind of recurrence condition which is satisfied by almost periodic perturbations. Following a functional analytic approach we construct a Melnikov-like function M(α) in such a way that if M(α) has a simple zero at some point, then the system has solutions that behave chaotically. Applications of this result to quasi-periodic systems are also given.
Bifurcation and chaos near sliding homoclinics / Battelli, Flaviano; M., Feckan. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 248:(2010), pp. 2227-2262.
Bifurcation and chaos near sliding homoclinics
BATTELLI, Flaviano;
2010-01-01
Abstract
The problem is studied of chaotic behaviour of a time dependent perturbation of a discontinuous differential equation whose unperturbed part has a sliding homoclinic orbit that is a solution homoclinic to a hyperbolic fixed point with a part belonging to a discontinuity surface. It is assumed that the time dependent perturbation satisfies a kind of recurrence condition which is satisfied by almost periodic perturbations. Following a functional analytic approach we construct a Melnikov-like function M(α) in such a way that if M(α) has a simple zero at some point, then the system has solutions that behave chaotically. Applications of this result to quasi-periodic systems are also given.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
