This paper proposes a novel technique to obtain sufficient conditions for the existence and stabilization of positive solutions for a kind of hyper-chaotic financial model. Since some important economic indexes are heavily related to region, the authors consider a nonlinear chaotic financial system with diffusion, which leads to some mathematical difficulties in dealing with the infinite-dimension characteristic. In order to overcome these difficulties, novel analysis techniques have to be proposed on the basis of Laplacian semigroup and impulsive control. Sufficient conditions are provided for existence and global exponential stabilization of positive solution for the system. It is interesting to discover that the impulse strength can be larger than 1 in the newly obtained stability criterion. Numerical simulations show the effectiveness of theoretical analysis.
This paper reports a new global Mittag-Leffler synchronization criterion with regard to fractional-order hyper-chaotic financial systems by designing the suitable impulsive control and the state feedback controller. The significance of this impulsive synchronization lies in the fact that the backward economic system can synchronize asymptotically with the advanced economic system under effective impulse macroeconomic management means. Matlab’s LMI toolbox is utilized to deduce the feasible solution in a numerical example, which shows the effectiveness of the proposed methods. It is worth mentioning that the LMI-based criterion usually requires the activation function of the system to be Lipschitz, but the activation function in this paper is fixed and truly nonlinear, which cannot be assumed to be Lipschitz continuous. This is another mathematical difficulty overcome in this paper.
The fixed point technique has been employed in the stability analysis of time-delays bidirectional associative memory (BAM) neural networks with impulse. By formulating a contraction mapping in a product space, a new LMI-based exponential stability criterion was derived. Lately, fixed point methods have educed various good results inspiring this work, but those criteria cannot be programmed by a computer. In this paper, LMI conditions of the obtained result can be applicable to computer Matlab LMI toolbox which meets the need of the large-scale calculation in real engineering. Moreover, a numerical example and a comparable table are presented to illustrate the effectiveness of the proposed methods.
This paper reports a new global Mittag-Leffler synchronization criterion with regard to fractional-order hyper-chaotic financial systems by designing the suitable impulsive control and the state feedback controller. The significance of this impulsive synchronization lies in the fact that the backward economic system can synchronize asymptotically with the advanced economic system under the effective impulse macroeconomic management means. Matlab LMI-toolbox is utilized to deduce the feasible solution in numerical example, which shows the effectiveness of the proposed methods. It is worth mentioning that the LMI-based criterion usually requires the activation function of the system to be Lipschitz, but the activation function in this paper is fixed and truly nonlinear, which cannot be assumed to be Lipschitz continuous. This is another mathematical difficulty overcome in this paper.
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