Hopf bifurcation, chaos control and synchronization of a chaotic fractional-order system with chaos entanglement function

2020 ◽  
Vol 172 ◽  
pp. 321-340 ◽  
Author(s):  
Shiva Eshaghi ◽  
Reza Khoshsiar Ghaziani ◽  
Alireza Ansari
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Order ◽  
Chaos Control ◽  
Fractional Order System ◽  
Order System ◽  
Control And Synchronization ◽  
Bifurcation Chaos

scholarly journals Complexity and Hopf Bifurcation Analysis on a Kind of Fractional-Order IS-LM Macroeconomic System

2016 ◽  
Vol 26 (11) ◽  
pp. 1650181 ◽  
Author(s):  
Junhai Ma ◽  
Wenbo Ren
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Order ◽  
Dynamic Characteristics ◽  
Fractional Order System ◽  
Order System ◽  
Complex Dynamic ◽  
Macroeconomic Regulation And Control ◽  
And Control ◽  
System Order ◽  
Macroeconomic Environment

On the basis of our previous research, we deepen and complete a kind of macroeconomics IS-LM model with fractional-order calculus theory, which is a good reflection on the memory characteristics of economic variables, we also focus on the influence of the variables on the real system, and improve the analysis capabilities of the traditional economic models to suit the actual macroeconomic environment. The conditions of Hopf bifurcation in fractional-order system models are briefly demonstrated, and the fractional order when Hopf bifurcation occurs is calculated, showing the inherent complex dynamic characteristics of the system. With numerical simulation, bifurcation, strange attractor, limit cycle, waveform and other complex dynamic characteristics are given; and the order condition is obtained with respect to time. We find that the system order has an important influence on the running state of the system. The system has a periodic motion when the order meets the conditions of Hopf bifurcation; the fractional-order system gradually stabilizes with the change of the order and parameters while the corresponding integer-order system diverges. This study has certain significance to policy-making about macroeconomic regulation and control.

Stability and Hopf bifurcation analysis of a biotic resource enrichment on a prey predator population in fractional-order system

2021 ◽  
Author(s):  
Abiodun Ezekiel Owoyemi ◽  
Ibrahim Mohammed Sulaiman ◽  
Salisu Sadiya Muhammad ◽  
Oluwatayo Olatunde Oni ◽  
Olukayode Williams Okedokun
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Order ◽  
Bifurcation Analysis ◽  
Fractional Order System ◽  
Order System ◽  
Predator Population ◽  
Biotic Resource

scholarly journals Coexisting Three-Scroll and Four-Scroll Chaotic Attractors in a Fractional-Order System by a Three-Scroll Integer-Order Memristive Chaotic System and Chaos Control

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Xikui Hu ◽  
Ping Zhou
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Chaos Control ◽  
Initial Conditions ◽  
Fractional Order System ◽  
Order System ◽  
Chaotic Attractors ◽  
Integer Order ◽  
Memristive System ◽  
Fractional Orders

Based on the integer-order memristive system that can generate two-scroll, three-scroll, and four-scroll chaotic attractors, in this paper, we found other phenomena that two kinds of three-scroll chaotic attractors coexist in this system with different initial conditions. Furthermore, we proposed a coexisting fractional-order system based on the three-scroll chaotic attractors system, in which the three-scroll or four-scroll chaotic attractors emerged with different fractional-orders q. Meanwhile, with fractional-order q=0.965 and different initial conditions, coexistence of two kinds of three-scroll and four-scroll chaotic attractors is found simultaneously. Finally, we discussed controlling chaos for the fractional-order memristive chaotic system.

scholarly journals CHAOS CONTROL AND SYNCHRONIZATION USING SYNERGETIC CONTROLLER WITH FRACTIONAL AND LINEAR EXTENDED MANIFOLD

2016 ◽  
Vol 17 (1) ◽  
pp. 115-126
Author(s):  
Morteza Pourmehdi ◽  
Abolfazl Ranjbar Noei ◽  
Jalil Sadati
Keyword(s):  
Fractional Order ◽  
Chaos Control ◽  
Order System ◽  
State Variables ◽  
System Quality ◽  
Control Effort ◽  
Lower Amplitude ◽  
The Stability ◽  
Fractional Order Controller ◽  
Control And Synchronization

In this manuscript, for the first time, a fractional-order manifold in a synergetic approach using a fractional order controller is introduced. Furtheremore, in the synergetic theory a macro variable is expended into a linear combination of state variables. An aim is to increase the convergence rate as well as time response of the whole closed loop system. Quality of the proposed controller is investigated to control and synchronize a nonlinear chaotic Coullet system in comparison with an integer order manifold synergetic controller. The stability of the proposed controller is proven using the Lyapunov method. In this regard stabilizing control effort is yielded. Simulation result confirm convergence of states towards zero. This is achieved through a control effort with fewer oscillations and lower amplitude of signls which confirm feasibility of the control effort in practice.KEYWORDS:  synergetic control theory; fractional order system; synchronization; nonlinear chaotic Coullet system; chaos control

Adaptive Synchronization of a Stochastic Fractional-Order System

2015 ◽  
Vol 733 ◽  
pp. 939-942
Author(s):  
Xiao Jun Liu
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Stochastic System ◽  
Fractional Order System ◽  
Adaptive Synchronization ◽  
Order System ◽  
Unknown Parameters ◽  
Adaptive Laws

In this paper, adaptive synchronization of a stochastic fractional-order system with unknown parameters is studied. Firstly, the stochastic system is reduced into the equivalent deterministic one with Laguerre approximation. Then, the synchronization for the system is realized by designing appropriate controllers and adaptive laws of the unknown parameters. Numerical simulations are carried out to demonstrate the effectiveness of the controllers and laws.

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