Bifurcations and Exact Bounded Solutions of Some Travelling Wave Systems Determined by Integrable Nonlinear Oscillators with q-Degree Damping

讲座时间 Datetime: 2022年9月8日，星期四，15:00-16:00

地点 Venue: 腾讯线上会议：886-143-490

主持人 Host：刘长剑

报告人 Speaker: 李继彬

单位 Affiliation: 华侨大学

报告摘要 Abstract:

题目：For a class of nonlinear diffusion-convection-reaction equations, the corresponding travelling wave systems are well known nonlinear oscillation type systems. Under some parameter conditions, the first integrals of these nonlinear oscillators can be obtained. In this talk, we use the method of dynamical systems to study the bifurcations, exact solutions and dynamical behavior for these nonlinear oscillators.  Under given parametric conditions, some exact explicit parametric representations of the monotonic and non-monotonic kink and anti-kink wave solutions, limit cycles are obtained. A new global bifurcation phenomenon of limit bifurcation is found: with a parameter is varied, by the singular points disappear (it is not the origin), planar dynamical system can create a stable limit cycle.