Math. Model. Nat. Phenom.
Volume 8, Number 5, 2013Bifurcations
|155 - 172
|17 September 2013
Dynamical Features in a Slow-fast Piecewise Linear Hamiltonian System
Lobachevsky State University of Nizhni Novgorod,
2 The State University of Management, Moscow, Russia
⋆ Corresponding author. E-mail: firstname.lastname@example.org
We demonstrate that a piecewise linear slow-fast Hamiltonian system with an equilibrium of the saddle-center type can have a sequence of small parameter values for which a one-round homoclinic orbit to this equilibrium exists. This contrasts with the well-known findings by Amick and McLeod and others that solutions of such type do not exist in analytic Hamiltonian systems, and that the separatrices are split by the exponentially small quantity. We also discuss existence of homoclinic trajectories to small periodic orbits of the Lyapunov family as well as symmetric periodic orbits near the homoclinic connection. Our further result, illustrated by simulations, concerns the complicated structure of orbits related to passage through a non-smooth bifurcation of a periodic orbit.
Mathematics Subject Classification: 34A36 / 34C23 / 34C37 / 34C28 / 34E15 / 70K70 / 74H65
Key words: slow-fast system / Hamiltonian / piecewise linear / homoclinic / periodic / nonsmooth bifurcation
© EDP Sciences, 2013
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.