ON SYNCHRONIZATION AND CONTROL OF COUPLED WILSON–COWAN NEURAL OSCILLATORS

2003 ◽  
Vol 13 (01) ◽  
pp. 163-175 ◽  
Author(s):  
TETSUSHI UETA ◽  
GUANRONG CHEN
Keyword(s):  
Control Method ◽  
Complex Dynamics ◽  
Mapping Method ◽  
Control Of Chaos ◽  
Neural Oscillators ◽  
Higher Dimensional ◽  
Strongly Connected ◽  
Feedback Control Method ◽  
And Control ◽  
Simple Feedback

This paper investigates the complex dynamics, synchronization and control of chaos in a system of strongly connected Wilson–Cowan neural oscillators. Some typical synchronized periodic solutions are analyzed by using the Poincaré mapping method, for which bifurcation diagrams are obtained. It is shown that topological change of the synchronization mode is mainly caused and carried out by the Neimark–Sacker bifurcation. Finally, a simple feedback control method is presented for stabilizing an in-phase synchronizing periodic solution embedded in the chaotic attractor of a higher-dimensional model of such coupled neural oscillators.

scholarly journals Adaptive Control of Chaos in Chua's Circuit

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Weiping Guo ◽  
Diantong Liu
Keyword(s):  
Feedback Control ◽  
Control Method ◽  
Equilibrium Points ◽  
Lyapunov Theory ◽  
Chua’S Circuit ◽  
Control Of Chaos ◽  
Chua's Circuit ◽  
Adaptive Technology ◽  
Feedback Control Method ◽  
And Control

A feedback control method and an adaptive feedback control method are proposed for Chua's circuit chaos system, which is a simple 3D autonomous system. The asymptotical stability is proven with Lyapunov theory for both of the proposed methods, and the system can be dragged to one of its three unstable equilibrium points respectively. Simulation results show that the proposed methods are valid, and control performance is improved through introducing adaptive technology.

scholarly journals Bifurcation and Chaos of a Discrete Predator-Prey Model with Crowley–Martin Functional Response Incorporating Proportional Prey Refuge

2020 ◽  
Vol 2020 ◽  
pp. 1-18 ◽  
Author(s):  
P. K. Santra ◽  
G. S. Mahapatra ◽  
G. R. Phaijoo
Keyword(s):  
Functional Response ◽  
Control Method ◽  
Equilibrium Points ◽  
Period Doubling ◽  
Phase Portraits ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Feedback Control Method ◽  
And Control

The paper investigates the dynamical behaviors of a two-species discrete predator-prey system with Crowley–Martin functional response incorporating prey refuge proportional to prey density. The existence of equilibrium points, stability of three fixed points, period-doubling bifurcation, Neimark–Sacker bifurcation, Marottos chaos, and Control Chaos are analyzed for the discrete-time domain. The time graphs, phase portraits, and bifurcation diagrams are obtained for different parameters of the model. Numerical simulations and graphics show that the discrete model exhibits rich dynamics, which also present that the system is a chaotic and complex one. This paper attempts to present a feedback control method which can stabilize chaotic orbits at an unstable equilibrium point.

Control of Oscillations of a Wing Subjected to 3D Unsteady Subsonic Aerodynamic Loads Using Piezoelectric Actuators

2012 ◽  
Author(s):  
Tahereh Mirmohammadi ◽  
Arun K. Misra ◽  
Dan Mateescu
Keyword(s):  
Control Method ◽  
Three Dimensional ◽  
Element Formulation ◽  
Sensors And Actuators ◽  
Aerodynamic Loading ◽  
Aerodynamic Model ◽  
Active Feedback ◽  
Feedback Control Method ◽  
And Control ◽  
Actuator Placement

In the recent years, using piezoelectric material as sensors and actuators has drawn significant attention in vibration analysis and control of structures. In the present paper, bonded piezoelectric sensors and actuators have been used to control the aeroelastic oscillations of a cantilever wing under the effects of three-dimensional unsteady subsonic aerodynamic loading. An aerodynamic model using a numerical panel method is developed and validated to calculate the three-dimensional unsteady aerodynamic loading and finite element formulation is applied to model the wing structure as a cantilever plate undergoing small transverse oscillations. The structural and aerodynamic models are combined to simulate the aeroelastic oscillations and interchange the data simultaneously. An active feedback control method to suppress the oscillations is presented and investigated. Finally, an analysis is performed to examine the effects of actuator placement on the wing surface in suppression of oscillations.

scholarly journals Study on Triopoly Dynamic Game Model Based on Different Demand Forecast Methods in the Market

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Junhai Ma ◽  
Lijian Sun ◽  
Xueli Zhan
Keyword(s):  
Control Method ◽  
Complex Dynamics ◽  
Dynamic Game ◽  
Basins Of Attraction ◽  
Attraction Domain ◽  
Stable Region ◽  
Demand Forecast ◽  
Feedback Control Method ◽  
Set Up ◽  
The Impact

The impact of inaccurate demand beliefs on dynamics of a Triopoly game is studied. We suppose that all the players make their own estimations on possible demand with errors. A dynamic Triopoly game with such demand belief is set up. Based on this model, existence and local stable region of the equilibriums are investigated by 3D stable regions of Nash equilibrium point. The complex dynamics, such as bifurcation scenarios and route to chaos, are displayed in 2D bifurcation diagrams, in which e1 and α are negatively related to each other. Basins of attraction are investigated and we found that the attraction domain becomes smaller with the increase in price modification speed, which indicates that all the players’ output must be kept within a certain range so as to keep the system stable. Feedback control method is used to keep the system at an equilibrium state.

scholarly journals Bifurcation Analysis and Control of a Differential-Algebraic Predator-Prey Model with Allee Effect and Time Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Xue Zhang ◽  
Qing-ling Zhang
Keyword(s):  
Time Delay ◽  
Allee Effect ◽  
Control Method ◽  
Handling Time ◽  
Delayed Feedback Control ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Feedback Control Method ◽  
Predator Model ◽  
And Control

This paper studies systematically a differential-algebraic prey-predator model with time delay and Allee effect. It shows that transcritical bifurcation appears when a variation of predator handling time is taken into account. This model also exhibits singular induced bifurcation as the economic revenue increases through zero, which causes impulsive phenomenon. It can be noted that the impulsive phenomenon can be much weaker by strengthening Allee effect in numerical simulation. On the other hand, at a critical value of time delay, the model undergoes a Hopf bifurcation; that is, the increase of time delay destabilizes the model and bifurcates into small amplitude periodic solution. Moreover, a state delayed feedback control method, which can be implemented by adjusting the harvesting effort for biological populations, is proposed to drive the differential-algebraic system to a steady state. Finally, by using Matlab software, numerical simulations illustrate the effectiveness of the results.

scholarly journals Hopf Bifurcation and Control of Magnetic Bearing System with Uncertain Parameter

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Jing Wang ◽  
Shaojuan Ma ◽  
Peng Hao ◽  
Hehui Yuan
Keyword(s):  
Hopf Bifurcation ◽  
Feedback Control ◽  
Control Method ◽  
Magnetic Bearing ◽  
Uncertain Parameter ◽  
Equivalent Model ◽  
Linear Feedback ◽  
Feedback Control Method ◽  
And Control ◽  
Bearing System

In this paper, the Hopf bifurcation and control of the magnetic bearing system under an uncertain parameter are investigated. Firstly, the two-degree-of-freedom magnetic bearing system model with uncertain parameter is established. The method of orthogonal polynomial approximation is used to obtain the equivalent magnetic bearing model which is deterministic. Secondly, combining mathematical analysis tools and numerical simulations, the Hopf bifurcation of the equivalent model is analyzed. Finally, a hybrid feedback control method (linear feedback control method combined with nonlinear stochastic feedback control method) is introduced to control the Hopf bifurcation behavior of the magnetic bearing system.

BIFURCATION ANALYSIS AND CONTROL OF A PLANKTON–FISH MODEL WITH A DISTRIBUTION DELAY

2011 ◽  
Vol 11 (04) ◽  
pp. 857-879 ◽  
Author(s):  
XUE ZHANG ◽  
QINGLING ZHANG
Keyword(s):  
Center Manifold ◽  
Control Method ◽  
Distributed Delay ◽  
State Feedback Control ◽  
Positive Equilibrium ◽  
Center Manifold Theorem ◽  
Fish Model ◽  
Feedback Control Method ◽  
Positive Equilibrium Point ◽  
And Control

This paper studies a plankton–fish model with distributed delay in the context of marine plankton interaction together with predation by planktotrophic fish. The delay indicates that the growth of the zooplankton depends on the past density of phytoplankton. The positive equilibrium point and its local stability are investigated. Using the average time delay as bifurcation parameter, we obtain the conditions of the existence of Hopf bifurcation. Based on the normal form and center manifold theorem, stability, direction, and other properties of bifurcating periodic solutions are derived. Moreover, a state feedback control method, which can be implemented by adjusting the harvesting for zooplankton population, is proposed to drive the plankton–fish system to a steady state. Numerical simulations illustrate the effectiveness of results and the related biological implications are discussed.

Anti-Control of Chaos of Linear Continuous-Time Systems with Unknown Parameters Using Adaptive Control

2011 ◽  
Vol 403-408 ◽  
pp. 4806-4813
Author(s):  
Farzaneh Akhgari ◽  
Zahra Rahmani ◽  
Behrooz Rezaie
Keyword(s):  
Linear System ◽  
Control Method ◽  
Reference Model ◽  
Lyapunov Stability Theory ◽  
Model Matching ◽  
Control Of Chaos ◽  
Unknown Parameters ◽  
Feedback Control Method ◽  
The Stability ◽  
Controllable Systems

In this paper, a feedback control method is proposed for the anti-control of chaos of linear controllable systems based on model-matching. First, it is considered that the linear system is completely known and an anti-control method is designed. Then, the parameters of the linear controllable system in companion form are assumed to be unknown. The chaotification is achieved choosing an appropriate control law and a parametric updating law based on Lyapunov stability theory, which provides the stability of the resulting adaptive system and the convergence of the tracking errors to zero. The proposed method is applied to anti-control of chaos of a linear system, while the Rössler chaotic system is the reference model. The numerical simulation results show the effectiveness of the proposed method.

scholarly journals Analysis of Complex Dynamics in Different Bargaining Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Xiaogang Ma ◽  
Chunyu Bao ◽  
Lin Su
Keyword(s):  
Supply Chain ◽  
Collective Bargaining ◽  
Control Method ◽  
Complex Dynamics ◽  
Control Factor ◽  
Feedback Control Method ◽  
Delay Feedback Control ◽  
The Stability ◽  
Risk And Benefit ◽  
Bargaining Behavior

This paper focuses on the bargaining behavior of supply chain members and studies the stability of the bargaining system. There are two forms of bargaining in the process of negotiation. One is separate bargaining, and the other is that the automobile manufacturers form an alliance and bargain with the supplier collectively. We explore the influence of bargaining power and adjustment speed on the stability of the dynamic system and find that both of the factors need to be small to maintain the stability of the supply chain. After comparing the two forms of bargaining in terms of profits and stable regions, we find that the collective bargaining is a pattern with the existence of risk and benefit simultaneously. In order to control chaos in collective bargaining to lower the risk, we adopt the delay feedback control method. With the introduction of the control factor, the system tends to be stable finally.

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