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.

FOLD–HOPF BIFURCATION ANALYSIS FOR A COUPLED FITZHUGH–NAGUMO NEURAL SYSTEM WITH TIME DELAY

2010 ◽  
Vol 20 (12) ◽  
pp. 3919-3934 ◽  
Author(s):  
BIN ZHEN ◽  
JIAN XU
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Bifurcation Analysis ◽  
Signal Transmission ◽  
Neural System ◽  
Center Manifold Reduction ◽  
Delayed Coupling ◽  
Normal Form Method ◽  
Manifold Reduction ◽  
System With Time Delay

A FitzHugh–Nagumo (FHN) model with delayed coupling is considered. For a critical case when the corresponding characteristic equation has a single zero root and a pair of purely imaginary roots, a complete bifurcation analysis is presented by employing the center manifold reduction and the normal form method. The Fold–Hopf bifurcation diagrams are provided to illustrate the correctness of our theoretical analysis. Whether almost periodic motion and bursting behavior occur in the FHN neural system with delayed coupling depends on the time delay in the signal transmission between the neurons.

scholarly journals Bifurcation Analysis of a Fractional-Order Delayed Rolling Mill’s Main Drive Electromechanical Coupling System

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Rui Zhang ◽  
Jinbin Wang ◽  
Lifeng Ma
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Bifurcation Analysis ◽  
Electromechanical Coupling ◽  
System Stability ◽  
Coupling System

This work is focused on a rolling mill’s main drive electromechanical coupling system. Firstly, we equip electromechanical coupling system with fractional-order time delay. Secondly, we, respectively, derive the conditions for occurrence of Hopf bifurcation around equilibriums E 0 0 , 0 , 0 , 0 and E 1 x 1 ∗ , 0 , x 3 ∗ , 0 . It is found that the fractional order α and time delay τ in the system play an important role on the system stability. Finally, numerical simulations are given to verify the analytic results.

scholarly journals Bifurcation Based-Delay Feedback Control Strategy for a Fractional-Order Two-Prey One-Predator System

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Shuai Li ◽  
Chengdai Huang ◽  
Xinyu Song
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Fractional Order ◽  
Feedback Gain ◽  
Controlled System ◽  
Delay Feedback Control ◽  
Feedback Control Strategy ◽  
System With Time Delay ◽  
Theoretical Results ◽  
Predator System

The issue of bifurcation control for a novel fractional-order two-prey and one-predator system with time delay is dealt with in this paper. Firstly, the characteristic equation is investigated by picking time delay as the bifurcation parameter, and some conditions for the appearance of Hopf bifurcation are obtained. It is shown that time delay can give rise to periodic oscillations and each order has an important impact on the occurrence of Hopf bifurcation for the controlled system. Then, it is illustrated that the control result is obviously influenced by the feedback gain. It is also noted that the inception of the bifurcation can be postponed if the feedback gain decreases. Finally, two simulation examples are carried out to verify the chief theoretical results.

scholarly journals Stability control of a novel multidimensional fractional-order financial system with time‐delay via impulse control

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Zhe Zhang ◽  
Jing Zhang ◽  
Fan Yong Cheng ◽  
Feng Liu ◽  
Can Ding
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Impulse Control ◽  
Impulsive Control ◽  
Financial System ◽  
Stability Control ◽  
Two Dimensions ◽  
State Variable ◽  
The Stability ◽  
System With Time Delay

AbstractThis paper is concerned about the impulsive control of a class of novel nonlinear fractional-order financial system with time-delay. Considering the variation of every states in the fractional-order financial system in the real world has certain delay for various reasons, thus we add corresponding delay on every state variable. Different from the traditional method of stability judgment, we choose two dimensions of time and space to analyze, which makes the process more accurate. In addition, the sufficient condition of the stability criterion for the fractional-order financial system based on impulsive control is derived. Moreover, the impulsive control can not only make the fractional-order financial system stable in different time delay but also in the different fractional operator. Consequently, the impulsive control has generality, universality and strong applicability. In the end, some numerical simulation examples are provided to verify the effectiveness and the benefit of the proposed method.

scholarly journals Stability and Hopf Bifurcation Analysis of a Fractional-Order Epidemic Model with Time Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Zhen Wang ◽  
Xinhe Wang
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Numerical Simulations ◽  
Equilibrium Point ◽  
Fractional Order ◽  
Bifurcation Analysis ◽  
Epidemic Model ◽  
Bifurcation Parameter ◽  
Theoretical Results ◽  
Disease Free

A fractional-order epidemic model with time delay is considered. Firstly, stability of the disease-free equilibrium point and endemic equilibrium point is studied. Then, by choosing the time delay as a bifurcation parameter, the existence of Hopf bifurcation is studied. Finally, numerical simulations are given to illustrate the effectiveness and feasibility of theoretical 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.

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