非线性生态系统的复杂动力学行为研究(Ⅱ)
Research on the Complicated Dynamical Behaviors of Nonlinear Ecosystems(Ⅱ)
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摘要: 本文是文献[1]的继续.主要讨论了非线性生态系统的一维简单模型所呈现出的复杂动力学行为:定点运动、周期运动和混沌运动等;简要论述了这种简单模型所显示出的复杂动力学行为的普适性,这可由M.Feigenbaum第一常数和第二常数描述.最后,本文还讨论了非线性生态系统在从未分岔状态逼近分岔点时会由于接近失稳而发生的“单边慢化现象”,这在生态资源的开发利用和人工生态系统的设计与管理中具有重要的理论意义和实践意义.Abstract: This paper is a further study of reference [1]. In this paper, we mainly discuss the complicated dynamical behaviors resulting from a simple one-dimensional model of nonlinear ecosystems: fixed point motion, periodic motion and chaotic motion etc., and briefly discuss the universality of the complicated dynamical behaviors, which can be described by the first and the second M. Feigenbaun constants. At last, we discuss the "one-side lowering phenomenon" due to near unstabilization when the nonlinear ecosystem approaches bifurcation points from unbifurcation side. It is of important theoretical and practical meanings both in the development and utilization of ecological resources ar.d in the design and management of artifilial ecosystems.
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[1] 昝廷全,非线性生态系统的复杂动力学行为研究(I),应用数学和力学,9,10 (1988),925-931 [2] May,M.,Theoretical Ecology Blackwell Scientific Publishers(1981).23-37. [3] Haken,H.,Synergetics:An Introduction,Springer(1977),59-173. [4] 昝廷全等,泛系生态来类生克分析,科学探索,3(1988), 47-48. [5] 昝廷全、赵松岭,途态系统的热力学理论,《首届全国熵与交叉科学学术会议论文集》,气象出版社(待出版). -
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