A Physical Dissipative System with a Poincaré Homoclinic Figure-Eight
We consider 2D diffeomorphisms with a homoclinic figure-eight to a dissipative saddle under a periodic forcing. These systems are natural simplified models of phenomena with forcing and dissipation. As a physical example we study the dynamics of a parametrically driven dissipative pendulum with a magnetic kick forcing acting on it.
KeywordsBifurcation Diagram Invariant Manifold Invariant Curve Bifurcation Problem Invariant Curf
This work has been supported by grants MTM2010-16425 (Spain) and 2009 SGR 67 (Catalonia). We thank J. Timoneda for the technical support on the computing facilities of the Dynamical Systems Group of the Universitat de Barcelona, largely used in this work.
- 5.Kuznetsov, Y.A.: Elements of applied bifurcation theory. In: Applied Mathematical Sciences, vol. 112, 3rd edn. Springer, New York (2004)Google Scholar
- 6.Turaev, D.V.: On a case of bifurcations of a contour composed by two homoclinic curves of a saddle. In: Methods of the Qualitative Theory of Differential Equations, pp. 162–175. Gorki State University Pub. (1984) (in Russian)Google Scholar
- 8.Zaslavsky, G.M., Filonenko, N.N.: Stochastic instability of trapped particles and conditions of applicability of the quasi-linear approximation. Sov. Phys. JETP 27, 851–857 (1968)Google Scholar