This paper studies the global bifurcation and Hopf bifurcation of one kind of complicated financial system with different parameter combinations. Conditions on which bifurcation happens, and the critical system struct...This paper studies the global bifurcation and Hopf bifurcation of one kind of complicated financial system with different parameter combinations. Conditions on which bifurcation happens, and the critical system structure when the system transforms from one kind of topological structure to another are studied as well. The criterion for identifying Hopf bifurcation under different parameter combinations is also given. The chaotic character of this system under quasi-periodic force is finally studied. The bifurcation structure graphs are given when two parameters of the combination are fixed while the other parameter varies. The presence and stability of 2 and 3 dimensional torus bifurcation are studied. All of the Lyapunov exponents of the system with different bifurcation parameters and routes leading the system to chaos with different parameter combinations are studied. It is of important theoretical and practical meaning to probe the intrinsic mechanism of such continuous complicated financial system and to find the macro control policies for such kind of system.展开更多
This paper is concerned with the existence and the analytical approximations of limit cycles in a three-dimensional nonlinear autonomous feedback control system.Based on three-dimensional Hopf bifurcation theorem,the ...This paper is concerned with the existence and the analytical approximations of limit cycles in a three-dimensional nonlinear autonomous feedback control system.Based on three-dimensional Hopf bifurcation theorem,the existence of limit cycles is first proved.Then the homotopy analysis method(HAM) is applied to obtain the analytical approximations of the limit cycle and its frequency.In deriving the higher-order approximations,the authors utilized the idea of a perturbation procedure proposed for limit cycles' approximation in van der Pol equation.By comparing with the numerical integration solutions,it is shown that the accuracy of the analytical results obtained in this paper is very high,even when the amplitude of the limit cycle is large.展开更多
基金This research was supported by the National Natural Science Foundation of China under Grant No.60641006.
文摘This paper studies the global bifurcation and Hopf bifurcation of one kind of complicated financial system with different parameter combinations. Conditions on which bifurcation happens, and the critical system structure when the system transforms from one kind of topological structure to another are studied as well. The criterion for identifying Hopf bifurcation under different parameter combinations is also given. The chaotic character of this system under quasi-periodic force is finally studied. The bifurcation structure graphs are given when two parameters of the combination are fixed while the other parameter varies. The presence and stability of 2 and 3 dimensional torus bifurcation are studied. All of the Lyapunov exponents of the system with different bifurcation parameters and routes leading the system to chaos with different parameter combinations are studied. It is of important theoretical and practical meaning to probe the intrinsic mechanism of such continuous complicated financial system and to find the macro control policies for such kind of system.
基金supported by the National Natural Science Foundations of China under Grant Nos.11201072 and 11102041the China Postdoctoral Science Foundation under Grant No.2011M500803Education Department of Fujian Province under Grant No.JA10065
文摘This paper is concerned with the existence and the analytical approximations of limit cycles in a three-dimensional nonlinear autonomous feedback control system.Based on three-dimensional Hopf bifurcation theorem,the existence of limit cycles is first proved.Then the homotopy analysis method(HAM) is applied to obtain the analytical approximations of the limit cycle and its frequency.In deriving the higher-order approximations,the authors utilized the idea of a perturbation procedure proposed for limit cycles' approximation in van der Pol equation.By comparing with the numerical integration solutions,it is shown that the accuracy of the analytical results obtained in this paper is very high,even when the amplitude of the limit cycle is large.
