CAJ | 학술논문

在齐次Neumann边界条件下,研究了Brusselator系统的Hopf分支问题.证明了当参数满足一定条件时,Brusselator常微分系统的平衡解和周期解是渐近稳定的,而相应的偏微分系统的空间齐次平衡解是不稳定的；如果适当选取参数,那么Brusselator偏微分系统出现Hopf分支.同时,利用中心流形定理证明了Hopf分支解的稳定性.最后给出一些数值模拟的例子以验证和补充理论分析结果.
재제차Neumann변계조건하,연구료Brusselator계통적Hopf분지문제.증명료당삼수만족일정조건시,Brusselator상미분계통적평형해화주기해시점근은정적,이상응적편미분계통적공간제차평형해시불은정적；여과괄당선취삼수,나요Brusselator편미분계통출현Hopf분지.동시,이용중심류형정리증명료Hopf분지해적은정성.최후급출일사수치모의적례자이험증화보충이론분석결과.
The Brusselator system subject to homogeneous Neumann boundary conditions is investigated.It is firstly shown that the homogeneous equilibrium solution becomes turing unstable or diffusively unstable when parameters are chosen properly.Then the existence of Hopf bifurcation to the ODE and PDE models is obtained.Examples of numerical simulations are also shown to support and supplement the analytical results.