Synchronization of Time Delayed Fractional Order Chaotic Financial System

Abstract

The research on a time delayed fractional order financial chaotic system is a hot issue. In this paper, synchronization of time delayed fractional order financial chaotic system is studied. Based on comparison principle of linear fractional equation with delay, by using a fractional order inequality, a sufficient condition is obtained to guarantee the synchronization of master-slave systems. An example is exploited to show the feasibility of the theoretical results.

Time-Delay Synchronization and Anti-Synchronization of Variable-Order Fractional Discrete-Time Chen–Rossler Chaotic Systems Using Variable-Order Fractional Discrete-Time PID Control

“…We present in this research paper the solution to the problem of synchronization [1] and anti-synchronization [2] of discrete chaotic systems described by systems of differential equations of a variable fractional order [3] with time delay [4]. This analysis is carried out for nonlinear systems with the Caputo derivative for systems of a variable fractional order [3].…”

Time-Delay Synchronization and anti-Synchronization of Variable-Order Fractional Discrete-Time of Chen-Rossler Chaotics Systems Using Variable-Order Fractional-Discrete Time PID Control

“…We present in this research article, the solution to the problem of synchronization [1] and anti-synchronization [2] of discrete chaotic systems described by systems of differential equations of variable fractional order [3] and with time delay [4], where this analysis is carried out for non-linear systems in the sense of the derivative of Caputo for systems of variable fractional order [3].…”

Hopf Bifurcation and Dynamic Analysis of an Improved Financial System with Two Delays

“…With the development and innovation of financial markets, scholars have found that it will be better to add time delay factor for describing the actual economic markets [27][28][29][30]. Chen [31] analyzed the complex nonlinear dynamics, such as periodicity, quasiperiodicity, and chaotic behavior in the delayed feedback of financial systems.…”

“…In addition, Ma and Chen [14] added the delayed feedback to the three variables of financial system and gave some results on the existence of Hopf bifurcation and the effect of delayed feedback. Based on political events and other human factors, some scholars have considered the impact of delay and feedback items (see [28,34]). In practice, financial behaviour is not only affected by a single time delay but often seems to be affected by multiple external shocks.…”