In this paper, we give some sufficient conditions of the instability for the fourth order linear differential equation with varied coefficient, at least one of the characteristic roots of which has positive real part,...In this paper, we give some sufficient conditions of the instability for the fourth order linear differential equation with varied coefficient, at least one of the characteristic roots of which has positive real part, by means of Liapunov's second method.展开更多
In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary co...In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary conditions on a non-uniform mesh. The proposed variable mesh approximation is directly applicable to the integro-differential equation with singular coefficients. We need not require any special discretization to obtain the solution near the singular point. The convergence analysis of a difference scheme for the diffusion convection equation is briefly discussed. The presented variable mesh strategy is applicable when the internal grid points of the solution space are both even and odd in number as compared to the method discussed by authors in their previous work in which the internal grid points are strictly odd in number. The advantage of using this new variable mesh strategy is highlighted computationally.展开更多
In this paper, a novel method to model, track control and synchronize the Rossler’s chaotic system is proposed. The fuzzy logical system is used so that the fuzzy inference rule is transferred into a type of variable...In this paper, a novel method to model, track control and synchronize the Rossler’s chaotic system is proposed. The fuzzy logical system is used so that the fuzzy inference rule is transferred into a type of variable coefficient nonlinear ordinary differential equation. Consequently the model of the chaotic system is obtained. Then a fuzzy tracking control and a fuzzy synchronization for chaotic systems is proposed as well. First, a known tracking control for the Rossler’s system is used in this paper. We represent the Rossler’s chaotic and control systems into fuzzy inference rules. Then the variable coefficient nonlinear ordinary differential equation is also got. Simulation results show that such an approach is effective and has a high precision.展开更多
基金Provincial Science and Technology Foundation of Guizhou
文摘In this paper, we give some sufficient conditions of the instability for the fourth order linear differential equation with varied coefficient, at least one of the characteristic roots of which has positive real part, by means of Liapunov's second method.
文摘In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary conditions on a non-uniform mesh. The proposed variable mesh approximation is directly applicable to the integro-differential equation with singular coefficients. We need not require any special discretization to obtain the solution near the singular point. The convergence analysis of a difference scheme for the diffusion convection equation is briefly discussed. The presented variable mesh strategy is applicable when the internal grid points of the solution space are both even and odd in number as compared to the method discussed by authors in their previous work in which the internal grid points are strictly odd in number. The advantage of using this new variable mesh strategy is highlighted computationally.
文摘In this paper, a novel method to model, track control and synchronize the Rossler’s chaotic system is proposed. The fuzzy logical system is used so that the fuzzy inference rule is transferred into a type of variable coefficient nonlinear ordinary differential equation. Consequently the model of the chaotic system is obtained. Then a fuzzy tracking control and a fuzzy synchronization for chaotic systems is proposed as well. First, a known tracking control for the Rossler’s system is used in this paper. We represent the Rossler’s chaotic and control systems into fuzzy inference rules. Then the variable coefficient nonlinear ordinary differential equation is also got. Simulation results show that such an approach is effective and has a high precision.
