演講者：蔡宗龍教授

單　位：國立彰化師範大學數學系

日　期：2010年5月12日　PM 14:30

地　點：國立高雄大學理學院408室

講　題：Robust Heteroclinic Cycles and Frequency Locking

摘　要：

A heteroclinic cycle in a dynamical system is a topological cycle consisting of saddle-type equilibrium points, periodic orbits or chaotic attractors, and connecting trajectories between them. Normally, it is structurally unstable. However, in systems with some fixed sym-metric structure, heteroclinic cycles become robust. Applications of robust heteroclinic cycles can be found in various fields, such as eco-logical models of competing species, thermal convection, game theory and neuroscience. Symmetry-breaking perturbations may destroy heteroclinic cycles. In general, constant perturbations to a robust heteroclinic cycle result in periodic orbits. In this talk, we present the dynamics of a heteroclinc system with a periodic forcing, in which frequency-locking phenomena may be observed depending on the frequency of the forcing function. We prove that the system is equivalent to a circle map or a forced damped pendulum with torque.