This paper gives the conditions for the existence of a globally stable equi-librium of rz-dimensional Lotka-Volterra systems in the following cases: Lotka-Volterra chain systems and Lotka-Volterra modei between one an...This paper gives the conditions for the existence of a globally stable equi-librium of rz-dimensional Lotka-Volterra systems in the following cases: Lotka-Volterra chain systems and Lotka-Volterra modei between one and multispecies. The conditions obtained in this paper are much weaker than those in [6] and more easily verifiable in application. So the results can be applied to more general Lotka-Volterra models. At the same time, the existence and stability conditions of positive equilibrium points of the above systems are given.展开更多
We study the complete synchronization between different systems. Based on our new idea about structure adaptation, a new synchronized method, i.e. the structure adaptive method, is proposed. We believe that this self-...We study the complete synchronization between different systems. Based on our new idea about structure adaptation, a new synchronized method, i.e. the structure adaptive method, is proposed. We believe that this self-adaptive mechanism correctly represents essential characteristics of self-adaptation in complex systems. We also show that this method is reasonable both from the coupling viewpoint in physics and from the controller design viewpoint in control theory.展开更多
Under the assumptions that there exists exchange between cooperation and competition in some ecological systems, the paper provides a modei based on the Lotka-Volterra equations to describe the exchange in a two-dimen...Under the assumptions that there exists exchange between cooperation and competition in some ecological systems, the paper provides a modei based on the Lotka-Volterra equations to describe the exchange in a two-dimensional system. Then dynamics of the model is studied in detail, the division of distinct regions associated with difFerent dynamics in the parameter space is obtained, and the biological significance of these dynamical properties represent is discussed.展开更多
基金Supported by the NNSF of China (19972058) the NSF of Yunnan Province of China (2001A0001M).
文摘This paper gives the conditions for the existence of a globally stable equi-librium of rz-dimensional Lotka-Volterra systems in the following cases: Lotka-Volterra chain systems and Lotka-Volterra modei between one and multispecies. The conditions obtained in this paper are much weaker than those in [6] and more easily verifiable in application. So the results can be applied to more general Lotka-Volterra models. At the same time, the existence and stability conditions of positive equilibrium points of the above systems are given.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10372054 and 70431002.
文摘We study the complete synchronization between different systems. Based on our new idea about structure adaptation, a new synchronized method, i.e. the structure adaptive method, is proposed. We believe that this self-adaptive mechanism correctly represents essential characteristics of self-adaptation in complex systems. We also show that this method is reasonable both from the coupling viewpoint in physics and from the controller design viewpoint in control theory.
基金Suppotted by the NNSF of China(19972058) and the NSF of Yunnan Province(2001A0001M).
文摘Under the assumptions that there exists exchange between cooperation and competition in some ecological systems, the paper provides a modei based on the Lotka-Volterra equations to describe the exchange in a two-dimensional system. Then dynamics of the model is studied in detail, the division of distinct regions associated with difFerent dynamics in the parameter space is obtained, and the biological significance of these dynamical properties represent is discussed.
