耦合离散BVP振子的混沌现象

Chaos in discrete coupled BVP oscillators

应用动力系统的局部分支理论和混沌定理,研究耦合离散BVP系统当参数发生变化时产生的分支和Marotto混沌现象.利用不动点理论、分支理论和Marotto混沌定理,分析系统不动点的存在性,以及存在的音叉分支和鞍结分支,证明该系统Marotto混沌的存在性,并给出系统发生Marotto混沌所需条件.利用数值模拟得到该系统的分支图、最大Lyapunov指数图和相图,进一步展示该模型的复杂动态特性,验证耦合离散BVP系统存在音叉分支、鞍结分支和Marotto混沌.

This paper discussed bifurcation and Marotto chaos of the discrete resistively coupled BVP oscillators as the bifurcation parameters are changed by using bifurcation theories and chaos therom in dynamical systems.The system is analyzed by using the equilibrium theory,bifurcation theorem and Marottos chaos.Some conclusions about the existence of equilibrium,pitchfork bifurcation,saddle-node bifurcation and Marotto chaos are given.Several numerical simulations are provided to demonstrate the theoretical results.We find the discrete resistively coupled BVP oscillators existence for pitchfork bifurcation,saddle-node bifurcation and Marotto chaos.