Piecewise smooth dynamical systems: Persistence of periodic solutions and normal forms
Copyright policy )Piecewise smooth dynamical systems: Persistence of periodic solutions and normal forms
We consider an n-dimensional piecewise smooth vector field with two zones separated by a hyperplane \Sigma which admits an invariant hyperplane \Omega transversal to \Sigma containing a period annulus A fulfilled by crossing periodic solutions. For small discontinuous perturbations of these systems we develop a Melnikov-like function to control the persistence of periodic solutions contained in A. When n = 3 we provide normal forms for the piecewise linear case. Finally we apply the Melnikov-like function to study discontinuous perturbations of the given normal forms.
Averaging method for ordinary differential equations, piecewise differential system, Lyapunov-Schmidt reduction, Limit cycle, Discontinuous ordinary differential equations, Normal forms, Crossing periodic solutions, Limit cycles, limit cycle, normal form, Bifurcations of limit cycles and periodic orbits in dynamical systems, Periodic solutions to ordinary differential equations, Piecewise differential system, Transformation and reduction of ordinary differential equations and systems, normal forms, Crossing periodic orbits, crossing periodic solution
Averaging method for ordinary differential equations, piecewise differential system, Lyapunov-Schmidt reduction, Limit cycle, Discontinuous ordinary differential equations, Normal forms, Crossing periodic solutions, Limit cycles, limit cycle, normal form, Bifurcations of limit cycles and periodic orbits in dynamical systems, Periodic solutions to ordinary differential equations, Piecewise differential system, Transformation and reduction of ordinary differential equations and systems, normal forms, Crossing periodic orbits, crossing periodic solution
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