A Study on the Complexity of a New Chaotic Financial System

Abstract

The interaction of elements in a financial system can exhibit complex dynamic behaviours. In this article, we use a system of differential equations to model the evolution of a financial system and study its complexity. Numerical simulations show that the system exhibits a variety of rich dynamic behaviours, including chaos. Bifurcation diagrams show that the system behaves chaotically over a wide range of system parameters.

Adaptive Control of a New Chaotic Financial System with Integer Order and Fractional Order and Its Identical Adaptive Synchronization

“…In 2020, Liao et al [32] presented a new financial model in order to take into account the interaction between the interest rate x(t), the investment demand y(t), and the price index z(t). e system is defined as follows:…”

“…e study of dynamic behavior, and the control of chaos in financial and economic systems have also been approached in order to understand the dynamic behavior of these systems and stabilize them in order to eliminate undesirable behavior [10,[26][27][28][29][30][31]. In 2020, Liao et al [32] presented a new model to take into account the interaction between the various state variables of the system. e numerical study of this model revealed that it presents complex dynamic behaviors such as period doubling and chaos [32].…”

“…In 2020, Liao et al [32] presented a new model to take into account the interaction between the various state variables of the system. e numerical study of this model revealed that it presents complex dynamic behaviors such as period doubling and chaos [32]. It would therefore be interesting to control the chaos in this new financial system, in other words, to eliminate the undesirable behaviors of the system by considering the case where constant parameters of the system are unknown and also to carry out the identical adaptive synchronization of this new chaotic system.…”

“…In [32], when e � 0. [32]. e generalization of system (6), i.e., the fractional order version of the new financial system is also considered in this study.…”

Chaos control and synchronization of a new chaotic financial system with integer and fractional order

“…In [9], Chen et al designed simple linear feedback controllers to control and synchronize a fractional order financial system. In 2020, Liao et al [23] presented an alternative model to consider the interplay between the interest rate x(t), the investment demand y(t), and the price index z(t). The authors investigated this model using numerical simulations.…”