Dynamical Behaviors and Chaos in a New Fractional-order Financial System

2012 ◽  
Author(s):  
Zhoujin Cui ◽  
Pinneng Yu ◽  
Zong Wen
Keyword(s):  
Fractional Order ◽  
Financial System ◽  
Dynamical Behaviors

scholarly journals Chaos in a Financial System with Fractional Order and Its Control via Sliding Mode

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Paul Yaovi Dousseh ◽  
Cyrille Ainamon ◽  
Clément Hodévèwan Miwadinou ◽  
Adjimon Vincent Monwanou ◽  
Jean Bio Chabi Orou
Keyword(s):  
Fractional Order ◽  
Chaos Control ◽  
Sliding Mode ◽  
Financial System ◽  
Period Doubling ◽  
Fractional Order Systems ◽  
Uncertain Dynamics ◽  
Dynamical Behaviors ◽  
Order Case ◽  
Route To Chaos

In this paper, the dynamical behaviors and chaos control of a fractional-order financial system are discussed. The lowest fractional order found from which the system generates chaos is 2.49 for the commensurate order case and 2.13 for the incommensurate order case. Also, period-doubling route to chaos was found in this system. The results of this study were validated by the existence of a positive Lyapunov exponent. Besides, in order to control chaos in this fractional-order financial system with uncertain dynamics, a sliding mode controller is derived. The proposed controller stabilizes the commensurate and incommensurate fractional-order systems. Numerical simulations are carried out to verify the analytical results.

scholarly journals Corrigendum to “Chaos in a Financial System with Fractional Order and Its Control via Sliding Mode”

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Paul Yaovi Dousseh ◽  
Cyrille Ainamon ◽  
Clément Hodévèwan Miwadinou ◽  
Adjimon Vincent Monwanou ◽  
Jean Bio Chabi Orou
Keyword(s):  
Fractional Order ◽  
Chaos Control ◽  
Sliding Mode ◽  
Financial System ◽  
Period Doubling ◽  
Fractional Order Systems ◽  
Uncertain Dynamics ◽  
Dynamical Behaviors ◽  
Order Case ◽  
Route To Chaos

In this paper, the dynamical behaviors and chaos control of a fractional-order financial system are discussed. The lowest fractional order found from which the system generates chaos is 2.49 for the commensurate order case and 2.57 for the incommensurate order case. Also, the period-doubling route to chaos was found in this system. The results of this study were validated by the existence of a positive Lyapunov exponent. Besides, in order to control chaos in this fractional-order financial system with uncertain dynamics, a sliding mode controller is derived. The proposed controller stabilizes the commensurate and incommensurate fractional-order systems. Numerical simulations are carried out to verify the analytical results.

scholarly journals A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital Implementation

Inventions ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 49
Author(s):  
Zain-Aldeen S. A. Rahman ◽  
Basil H. Jasim ◽  
Yasir I. A. Al-Yasir ◽  
Raed A. Abd-Alhameed ◽  
Bilal Naji Alhasnawi
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Real World ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
State Variables ◽  
Digital Implementation ◽  
Dynamical Behaviors ◽  
Real World Applications

In this paper, a new fractional order chaotic system without equilibrium is proposed, analytically and numerically investigated, and numerically and experimentally tested. The analytical and numerical investigations were used to describe the system’s dynamical behaviors including the system equilibria, the chaotic attractors, the bifurcation diagrams, and the Lyapunov exponents. Based on the obtained dynamical behaviors, the system can excite hidden chaotic attractors since it has no equilibrium. Then, a synchronization mechanism based on the adaptive control theory was developed between two identical new systems (master and slave). The adaptive control laws are derived based on synchronization error dynamics of the state variables for the master and slave. Consequently, the update laws of the slave parameters are obtained, where the slave parameters are assumed to be uncertain and are estimated corresponding to the master parameters by the synchronization process. Furthermore, Arduino Due boards were used to implement the proposed system in order to demonstrate its practicality in real-world applications. The simulation experimental results were obtained by MATLAB and the Arduino Due boards, respectively, with a good consistency between the simulation results and the experimental results, indicating that the new fractional order chaotic system is capable of being employed in real-world applications.

scholarly journals Nonlinear Dynamics and Chaos in Fractional-Order Hopfield Neural Networks with Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xia Huang ◽  
Zhen Wang ◽  
Yuxia Li
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Fractional Order ◽  
Hopfield Neural Network ◽  
Hopfield Neural Networks ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Chaotic Motions ◽  
Dynamical Behaviors ◽  
Nonlinear Dynamics And Chaos

A fractional-order two-neuron Hopfield neural network with delay is proposed based on the classic well-known Hopfield neural networks, and further, the complex dynamical behaviors of such a network are investigated. A great variety of interesting dynamical phenomena, including single-periodic, multiple-periodic, and chaotic motions, are found to exist. The existence of chaotic attractors is verified by the bifurcation diagram and phase portraits as well.

Dynamic evolution characteristics of a fractional order hydropower station system

2018 ◽  
Vol 32 (02) ◽  
pp. 1750363 ◽  
Author(s):  
Xiang Gao ◽  
Diyi Chen ◽  
Donglin Yan ◽  
Beibei Xu ◽  
Xiangyu Wang
Keyword(s):  
Fractional Order ◽  
Careful Analysis ◽  
Hydropower Station ◽  
Dynamic Evolution ◽  
Engineering Practice ◽  
Shaft System ◽  
Dynamical Behaviors ◽  
Evolution Characteristics ◽  
Vertical Evolution ◽  
Hydropower Stations

This paper investigates the dynamic evolution characteristics of the hydropower station by introducing the fractional order damping forces. A careful analysis of the dynamic characteristics of the generator shaft system is carried out under different values of fractional order. It turns out the vibration state of the axis coordinates has a certain evolution law with the increase of the fractional order. Significantly, the obtained law exists in the horizontal evolution and vertical evolution of the dynamical behaviors. Meanwhile, some interesting dynamical phenomena were found in this process. The outcomes of this study enrich the nonlinear dynamic theory from the engineering practice of hydropower stations.

Dynamical Behaviors of a Fractional-Order Predator–Prey Model with Holling Type IV Functional Response and Its Discretization

2019 ◽  
Vol 20 (2) ◽  
pp. 125-136
Author(s):  
A. M. Yousef ◽  
S. Z. Rida ◽  
Y. Gh. Gouda ◽  
A. S. Zaki
Keyword(s):  
Functional Response ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Type Iv ◽  
Dynamical Behaviors ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Theoretical Results

AbstractIn this paper, we investigate the dynamical behaviors of a fractional-order predator–prey with Holling type IV functional response and its discretized counterpart. First, we seek the local stability of equilibria for the fractional-order model. Also, the necessary and sufficient conditions of the stability of the discretized model are achieved. Bifurcation types (include transcritical, flip and Neimark–Sacker) and chaos are discussed in the discretized system. Finally, numerical simulations are executed to assure the validity of the obtained theoretical results.

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