Impulsive Stabilization on Hyper-Chaotic Financial System under Neumann Boundary

Abstract

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.

Impulsive Control and Synchronization for Fractional-Order Hyper-Chaotic Financial System

“…Here, the parameters a, b, c, d and variables x, y, z, u can be referenced in detail in the literature ( [1][2][3][4][5]), Consider the corresponding response system as follows,…”

“…Set α = 1 in the systems ( 5) and (2). Equip System (2) and System (5) with the following data v1-eps-converted-to.pdf In fact, the corresponding data in Example 1 made financial systems chaos (see [1,[3][4][5]13]).…”

“…Hyperchaotic financial mathematical model includes the information of average profit margin, which simulates the actual complex and changeable financial market better, and has attracted much attention of researchers ( [1][2][3][4][5]). As what has been pointed out in [1,6], an extension of fractality concepts in the investigation of economic systems has been used.…”

“…11: Computer simulations of synchronization between x 4 and y 4 for α = 1 Remark 3. Fig.8-11 illustrate that the synchronization speeds of the financial systems in Example 2 are faster than those in Example 1, for the data a = 0.6, b = 0.3, c = 0.8, d = 0.1, k = 0.11 are different from those of Example 1.In fact, the corresponding data in Example 1 made financial systems chaos (see[1,[3][4][5]13]).…”

Impulsive Control and Synchronization for Fractional-Order Hyper-Chaotic Financial System

“…The hyperchaotic financial mathematical model takes into account the average profit margin, which can better simulate the actual complex and changeable financial market, and has attracted the attention of researchers ( [1][2][3][4][5]). As what has been pointed out in [1,6], an extension of fractality concepts in the investigation of the economic systems has been used.…”