Torus break-down and bifurcations in coupled oscillators

摘要

To discover qualitative changes of solutions of differential equations, one has to study their bifurcations. We start with the wellknown bifurcations of equilibria leading to periodic solutions, followed by bifurcations of periodic solutions (Neimark-Sacker and Hopf-Hopf) in a dissipative setting leading to quasi-periodic motion corresponding with tori. In their turn these families of quasi-periodic solutions may bifurcate to produce strange attractors. A number of examples illustrate the theory.