CAJ | 학술논문

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.
응용동력계통적국부분지이론화혼돈정리,연구우합리산BVP계통당삼수발생변화시산생적분지화Marotto혼돈현상.이용불동점이론、분지이론화Marotto혼돈정리,분석계통불동점적존재성,이급존재적음차분지화안결분지,증명해계통Marotto혼돈적존재성,병급출계통발생Marotto혼돈소수조건.이용수치모의득도해계통적분지도、최대Lyapunov지수도화상도,진일보전시해모형적복잡동태특성,험증우합리산BVP계통존재음차분지、안결분지화Marotto혼돈.
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.