6533b858fe1ef96bd12b65a2

RESEARCH PRODUCT

Coupled systems of non-smooth differential equations

Alain JacquemardDurval José Tonon

subject

Relay systemsLyapunov functionClass (set theory)Mathematics(all)Relay systemsDifferential equationGeneral MathematicsMathematical analysisOrder (ring theory)Non-smooth dynamical systemsNon smoothsymbols.namesakeReversibilitysymbolsPeriodic orbitsVector fieldMathematics

description

Abstract We study the geometric qualitative behavior of a class of discontinuous vector fields in four dimensions. Explicit existence conditions of one-parameter families of periodic orbits for models involving two coupled relay systems are given. We derive existence conditions of one-parameter families of periodic solutions of systems of two second order non-smooth differential equations. We also study the persistence of such periodic orbits in the case of analytic perturbations of our relay systems. These results can be seen as analogous to the Lyapunov Centre Theorem.

yearjournalcountryeditionlanguage
2012-04-01Bulletin des Sciences Mathématiques
10.1016/j.bulsci.2012.01.006http://dx.doi.org/10.1016/j.bulsci.2012.01.006