Lotka-Volterra系统的计算机辅助分析

Computer Aided Analysis for Lotka-Volterrra Systems

综述利用符号计算处理Lotka-Volterra系统周期轨道和平衡点的存在性和稳定性问题.考虑吴(特征列)方法在捕食系统方面的应用.利用实根分离算法来判断正平衡点的唯一性从而得到单调系统的整体稳定性.通过证明多项式系统的正定性得到离散扩散系统的整体稳定性.通过Liapunov方法和实根分离算法构造Kolmogorov系统的小扰动极限环.最后考虑三维系统极限环的算法化构造.

Symbolic manipulation for the existence of periodic orbits and the stability of Lotka-Voherrra systems is reviewed. Wu characteristic set method is discussed and applied to a class of prey-predator chain systems. Real root isolation algorithm is used to check the uniqueness of an equilibrium for a kind of monotone systems. The positiveness of a polynomial set implies the global stability of a class of diffusion systems. An algorithmic construction of limit cycles for 2D Kolmogorov and 3D Lotka-Volterra systems is mentioned.