一类自催化反应扩散系统平衡态的稳定与分歧

Stability of steady state and bifurcation in a autocatalytic reaction diffution system

目的研究一类自催化反应扩散系统平衡态的稳定性与分歧。方法根据线性化理论与弱的非线性理论,运用奇异摄动的方法进行研究。结果获得了该类反应模型平衡态局部稳定的充要条件与系统产生一致分歧解的必要条件。结论深化与丰富了稳定性理论。

Aim The stability of steady state and bifurcation in a autocatalytic reaction diffution system are to be studied. Methods According to the limearized theory and the weakly nonlinear theory, the perturbation method is used. Results A necessary and sufficient condition for the temopral stability of steady state is provided and the necessary conditon for the bifurcation of this steady state to spatially non-uniform solution is also given. Conclusion These resuhs deepen and enrich content of stability theory.