Bifurcation Analysis and Stability Criterion for the Nonlinear Fractional‐Order Three‐Dimensional Financial System with Delay

2018 ◽  
Vol 22 (1) ◽  
pp. 240-250 ◽  
Author(s):  
Zhe Zhang ◽  
Jing Zhang ◽  
Fanyong Cheng ◽  
Yuebing Xu
Keyword(s):  
Fractional Order ◽  
Bifurcation Analysis ◽  
Stability Criterion ◽  
Three Dimensional ◽  
Financial System ◽  
System With Delay

Julia Sets and Their Control in a Three-Dimensional Discrete Fractional-Order Financial Model

2021 ◽  
Vol 31 (16) ◽  
Author(s):  
Zhongyuan Zhao ◽  
Yongping Zhang
Keyword(s):  
Fixed Point ◽  
Fractional Order ◽  
Julia Set ◽  
Julia Sets ◽  
Three Dimensional ◽  
Financial System ◽  
Order Theory ◽  
System Model ◽  
Financial Model ◽  
Fractal Characteristics

It is of great significance to study the three-dimensional financial system model based on the discrete fractional-order theory. In this paper, the Julia set of the three-dimensional discrete fractional-order financial model is identified to show its fractal characteristics. The sizes of the Julia sets need to be changed in some situations, so it is necessary to achieve control of the Julia sets. In combination with the characteristics of the model, two different controllers based on the fixed point are designed, and the control of the three-dimensional Julia sets is realized by adding the controllers into the model in different ways. Finally, the simulation graphs show that the controllers can effectively control the fractal behaviors.

scholarly journals 0-1 Test for Chaos in a Fractional Order Financial System with Investment Incentive

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Baogui Xin ◽  
Yuting Li
Keyword(s):  
Fractional Calculus ◽  
Fractional Order ◽  
Three Dimensional ◽  
Financial System ◽  
Investment Incentive ◽  
Integer Order ◽  
System A ◽  
Weighted Integral ◽  
Test Algorithm ◽  
Predictor Corrector

A new integer-order chaotic financial system is extended by introducing a simple investment incentive into a three-dimensional chaotic financial system. A four-dimensional fractional-order chaotic financial system is presented by bringing fractional calculus into the new integer-order financial system. By using weighted integral thought, the fractional order derivative's economics meaning is given. The 0-1 test algorithm and the improved Adams-Bashforth-Moulton predictor-corrector scheme are employed to detect numerically the chaos in the proposed fractional order financial system.

scholarly journals Stability and Hopf bifurcation analysis of fractional order nonlinear financial system with time delay

2021 ◽  
Author(s):  
SANTOSHI PANIGRAHI ◽  
Sunita Chand ◽  
S Balamuralitharan
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Fractional Order ◽  
Bifurcation Analysis ◽  
Laplace Transformation ◽  
Financial System ◽  
System With Time Delay

In this paper, we study a fractional order time delay for nonlinear financial system. By using Laplace transformation, stability and Hopf bifurcation analysis have been done for the model. Furthermore, numerical simulation has been carried out for better understanding of our results.

Bifurcation Analysis of Fractional Order Single Cell with Delay

2015 ◽  
Vol 25 (02) ◽  
pp. 1550020 ◽  
Author(s):  
Vedat Çelik
Keyword(s):  
Neural Networks ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Single Cell ◽  
Fractional Order ◽  
Bifurcation Analysis ◽  
Stability Criterion ◽  
Order Model ◽  
Bifurcation Points ◽  
Fractional Order Model

This paper presents the bifurcation analysis of fractional order model of delayed single cell which is proposed for delayed cellular neural networks with respect to the time delay τ. The bifurcation points, time delay τc, are determined by modified Mikhailov stability criterion for a range of fractional delayed cell order 0.3 ≤ q < 1. Numerical results obtained from Adams–Bashforth–Moulton method demonstrate that the supercritical Hopf bifurcation occurs in the system.

BIFURCATION SCENARIO OF A THREE-DIMENSIONAL VAN DER POL OSCILLATOR

1993 ◽  
Vol 03 (02) ◽  
pp. 399-404 ◽  
Author(s):  
T. SÜNNER ◽  
H. SAUERMANN
Keyword(s):  
Bifurcation Diagram ◽  
Bifurcation Analysis ◽  
Chaotic Behavior ◽  
Three Dimensional ◽  
Global Bifurcation ◽  
Dynamical Behaviour ◽  
Van Der Pol Oscillator ◽  
Two Dimensional ◽  
Van Der Pol ◽  
Dimensional Models

Nonlinear self-excited oscillations are usually investigated for two-dimensional models. We extend the simplest and best known of these models, the van der Pol oscillator, to a three-dimensional one and study its dynamical behaviour by methods of bifurcation analysis. We find cusps and other local codimension 2 bifurcations. A homoclinic (i.e. global) bifurcation plays an important role in the bifurcation diagram. Finally it is demonstrated that chaos sets in. Thus the system belongs to the few three-dimensional autonomous ones modelling physical situations which lead to chaotic behavior.

HYPERCHAOS IN THE FRACTIONAL-ORDER NONAUTONOMOUS CHEN'S SYSTEM AND ITS SYNCHRONIZATION

2005 ◽  
Vol 16 (05) ◽  
pp. 815-826 ◽  
Author(s):  
HONGBIN ZHANG ◽  
CHUNGUANG LI ◽  
GUANRONG CHEN ◽  
XING GAO
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Chaotic System ◽  
Three Dimensional ◽  
Synchronization Problem ◽  
Driving Signal

Recently, a new hyperchaos generator, obtained by controlling a three-dimensional autonomous chaotic system — Chen's system — with a periodic driving signal, has been found. In this letter, we formulate and study the hyperchaotic behaviors in the corresponding fractional-order hyperchaotic Chen's system. Through numerical simulations, we found that hyperchaos exists in the fractional-order hyperchaotic Chen's system with order less than 4. The lowest order we found to have hyperchaos in this system is 3.4. Finally, we study the synchronization problem of two fractional-order hyperchaotic Chen's systems.

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