1. 毕业设计（论文）的内容和要求
考虑随机干扰因素对一类食饵--捕食者系统的动力学行为的影响。
通过构造Lyapunov 函数，给出确定性系统的正平衡点的全局渐近稳定性条件，及系统Hopf 分支出现的条件。
在随机干扰下，研究系统的全局正解是随机最终有界的和随机持久的，并给出随机渐近稳定性的充分条件。
2. 参考文献
1.Liu X and Han M A, Chaos and Hopf bifurcation analysis for a two species predator-prey system with prey refuge and diffusion, 2011 Nonlinear Anal.: Real World Applications 12 10472.Liu W and Wang K, Persistence and extinction in stochastic non-autonomous logistic systems, 2011 J. Math. Anal. Appl. 375 4433.Bandyopadhyay M and Chattopadhyay J, Ratio-dependent predator-prey model: effect of environmental fluctuation and stability, 2005 Nonlinearity 18 9134.Hou Z H, Yang L F, Zuo X B and Xin H W, Noise induced pattern transition and spatiotemporalstochastic resonance, 1998 Phys. Rev. Lett. 81 28545.Zhou C and Kurths J, Noise-sustained and controlled synchronization of stirred excitable media by external forcing, 2005 New J. Phys. 7 186.Kuang Y and Beretta E, Global qualitative analysis of a ratio-dependent predator-prey system, 1998 J. Math. Biol. 36 3897.Hsu S B, Hwang T W and Kuang Y, Global analysis of the Michaelis-Menten-type ratio-dependent predator-prey system, 2001 J. Math. Biol. 42 4898.Murray J D, Discussion: Turings theory of morphogenesis-its influence on modelling biologicalpattern and form, 1990 Bull. Math. Biol. 52 1179.D.Q. Jiang, N.Z. Shi, X.Y. Li, Global stability and stochastic permanence of a non-autonomous logistic equation with random perturbation, J. Math. Anal. Appl. 340 (2008) 588597.10.C.Y. Ji, D.Q. Jiang, X.Y. Li, Qualitative analysis of a stochastic ratiodependent predator-prey system, J. Comput. Appl. Math. 235 (2011) 13261341.11.M. Liu, K. Wang, Global stability of a nonlinear stochastic predatorprey system with Beddington-DeAngelis functional response, Commun. Nonlinear Sci. Numer. Simulat. 16 (2011) 11141121.
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