摘要
本文主要研究Brusselator系统的动力行为.首先,分析了系统产生Hopf分岔的原因,然后详细讨论了Brusselator系统平衡点的稳定性,并且证明了Brusselator系统当临界平衡点失稳时会产生超临界Hopf分岔,即从平衡点处分岔出稳定的极限环,进而得到了Brusselator系统出现Hopf分岔所需的参数条件;最后,数值模拟的结果显示了与理论分析的一致性.
The dynamical behavior of Brusselator system was considered. The mathematical mechanism of Hopf bifurcation was analyzed, and the stability of equilibrium was disscussed in detail. When the critical equilibrium loses its stability, supercritical Hopf bifurcation occurs. Hence, a stable periodic orbit bffrcates from the critical equilibrium. At the same time, the condition of parameter to ensure the appear of Hopf bifurcation in Bmsselator system was obtained. The result of numerical simulatior correspondented with that of theoretical analysis.
出处
《山东科学》
CAS
2007年第1期19-24,29,共7页
Shandong Science
