Downloads provided by UsageCountsStudy of Periodic Orbits in Periodic Perturbations of Planar Reversible Filippov Systems Having a Twofold Cycle
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Douglas D. Novaes; Tere M. Seara; Marco A. Teixeira; Iris O. Zeli;
Study of Periodic Orbits in Periodic Perturbations of Planar Reversible Filippov Systems Having a Twofold Cycle
We study the existence of periodic solutions in a class of planar Filippov systems obtained from non-autonomous periodic perturbations of reversible piecewise smooth differential systems. It is assumed that the unperturbed system presents a simple two-fold cycle, which is characterized by a closed trajectory connecting a visible two-fold singularity to itself. It is shown that under certain generic conditions the perturbed system has sliding and crossing periodic solutions. In order to get our results, Melnikov's ideas were applied together with tools from the geometric singular perturbation theory. Finally, a study of a perturbed piecewise Hamiltonian model is performed.
Differential equations, :37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory [Classificació AMS], periodic solutions, Equacions diferencials, Dynamical Systems (math.DS), piecewise smooth differential systems, 34A36, 34C23, 37G15, Filippov systems, twofold singularity, :34 Ordinary differential equations::34A General theory [Classificació AMS], FOS: Mathematics, Differentiable dynamical systems, sliding dynamics, Mathematics - Dynamical Systems, Bifurcation theory for ordinary differential equations, Àrees temàtiques de la UPC::Matemàtiques i estadística, Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory, Periodic solutions, Classificació AMS::34 Ordinary differential equations::34E Asymptotic theory, Nonautonomous smooth dynamical systems, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, :Matemàtiques i estadística [Àrees temàtiques de la UPC], :34 Ordinary differential equations::34E Asymptotic theory [Classificació AMS], Discontinuous ordinary differential equations, Sistemes dinàmics diferenciables, Perturbations, asymptotics of solutions to ordinary differential equations, Sliding dynamics, Piecewise smooth differential systems, Twofold singularity, Classificació AMS::34 Ordinary differential equations::34A General theory, Periodic solutions to ordinary differential equations
Differential equations, :37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory [Classificació AMS], periodic solutions, Equacions diferencials, Dynamical Systems (math.DS), piecewise smooth differential systems, 34A36, 34C23, 37G15, Filippov systems, twofold singularity, :34 Ordinary differential equations::34A General theory [Classificació AMS], FOS: Mathematics, Differentiable dynamical systems, sliding dynamics, Mathematics - Dynamical Systems, Bifurcation theory for ordinary differential equations, Àrees temàtiques de la UPC::Matemàtiques i estadística, Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory, Periodic solutions, Classificació AMS::34 Ordinary differential equations::34E Asymptotic theory, Nonautonomous smooth dynamical systems, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, :Matemàtiques i estadística [Àrees temàtiques de la UPC], :34 Ordinary differential equations::34E Asymptotic theory [Classificació AMS], Discontinuous ordinary differential equations, Sistemes dinàmics diferenciables, Perturbations, asymptotics of solutions to ordinary differential equations, Sliding dynamics, Piecewise smooth differential systems, Twofold singularity, Classificació AMS::34 Ordinary differential equations::34A General theory, Periodic solutions to ordinary differential equations
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