Exponential synchronization and stabilization of delayed feedback hyperchaotic financial system

Abstract

In a real financial market, the delayed market feedback and the delayed effect of government macrocontrol are inevitable, and both bring mathematical difficulties in studying stabilization and synchronization of the hyperchaotic financial system. However, employing the Lyapunov function method, differential mean value theorem, and suitable bounded hypotheses and pulse control technology result in globally asymptotic stabilization and synchronization criteria. It is the first paper driving the stabilization and synchronization criteria under the assumptions of double delays. Finally, numerical examples illustrate the effectiveness of the proposed methods.

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,…”

“…Example 2. 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.…”

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.…”

“…However, impulsive control is not considered in [1]. In fact, impulsive control is always one of the means of macroeconomic management ( [2,3]). In [2], a synchronization criterion of hyperchaotic financial system was derived by using impulsive control method and differential mean value theorem.…”