scholarly journals Chaos Control on a Duopoly Game with Homogeneous Strategy

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Manying Bai ◽  
Yazhou Gao
Keyword(s):  
Local Stability ◽  
Chaos Control ◽  
Control Method ◽  
Stable State ◽  
Delayed Feedback Control ◽  
Market Demand ◽  
Adaptive Expectation ◽  
Feedback Control Method ◽  
Simulation Results ◽  
Better Than

We study the dynamics of a nonlinear discrete-time duopoly game, where the players have homogenous knowledge on the market demand and decide their outputs based on adaptive expectation. The Nash equilibrium and its local stability are investigated. The numerical simulation results show that the model may exhibit chaotic phenomena. Quasiperiodicity is also found by setting the parameters at specific values. The system can be stabilized to a stable state by using delayed feedback control method. The discussion of control strategy shows that the effect of both firms taking control method is better than that of single firm taking control method.

scholarly journals Microcontroller Implementation, Chaos Control, Synchronization and Antisynchronization of Josephson Junction Model

2021 ◽  
Vol 1 (2) ◽  
pp. 198-208
Author(s):  
Rolande Tsapla Fotsa ◽  
André Rodrigue Tchamda ◽  
Alex Stephane Kemnang Tsafack ◽  
Sifeu Takougang Kingni
Keyword(s):  
Josephson Junction ◽  
Chaos Control ◽  
Control Method ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Hurwitz Stability ◽  
Feedback Control Method ◽  
Different Shapes ◽  
Simulation Results

The microcontroller implementation, chaos control, synchronization, and antisynchronization of the nonlinear resistive-capacitive-inductive shunted Josephson junction (NRCISJJ) model are reported in this paper. The dynamical behavior of the NRCISJJ model is performed using phase portraits, and time series. The numerical simulation results reveal that the NRCISJJ model exhibits different shapes of hidden chaotic attractors by varying the parameters. The existence of different shapes of hidden chaotic attractors is confirmed by microcontroller results obtained from the microcontroller implementation of the NRCISJJ model. It is theoretically demonstrated that the two designed single controllers can suppress the hidden chaotic attractors found in the NRCISJJ model. Finally, the synchronization and antisynchronization of unidirectional coupled NRCISJJ models are studied by using the feedback control method.  Thanks to the Routh Hurwitz stability criterion, the controllers are designed in order to control chaos in JJ models and achieved synchronization and antisynchronization between coupled NRCISJJ models. Numerical simulations are shown to clarify and confirm the control, synchronization, and antisynchronization.

BIFURCATION CONTROL OF A PARAMETRIC PENDULUM

2012 ◽  
Vol 22 (05) ◽  
pp. 1250111 ◽  
Author(s):  
ALINE S. DE PAULA ◽  
MARCELO A. SAVI ◽  
MARIAN WIERCIGROCH ◽  
EKATERINA PAVLOVSKAIA
Keyword(s):  
Chaos Control ◽  
Control Method ◽  
Excitation Frequency ◽  
Period Doubling ◽  
Bifurcation Control ◽  
Period Doubling Bifurcation ◽  
Delayed Feedback Control ◽  
Unstable Periodic Orbits ◽  
Parametric Pendulum ◽  
Feedback Control Method

In this paper, we apply chaos control methods to modify bifurcations in a parametric pendulum-shaker system. Specifically, the extended time-delayed feedback control method is employed to maintain stable rotational solutions of the system avoiding period doubling bifurcation and bifurcation to chaos. First, the classical chaos control is realized, where some unstable periodic orbits embedded in chaotic attractor are stabilized. Then period doubling bifurcation is prevented in order to extend the frequency range where a period-1 rotating orbit is observed. Finally, bifurcation to chaos is avoided and a stable rotating solution is obtained. In all cases, the continuous method is used for successive control. The bifurcation control method proposed here allows the system to maintain the desired rotational solutions over an extended range of excitation frequency and amplitude.

Projective synchronization via adaptive pinning control for fractional-order complex network with time-varying coupling strength

2019 ◽  
Vol 30 (07) ◽  
pp. 1940013
Author(s):  
Darui Zhu ◽  
Rui Wang ◽  
Chongxin Liu ◽  
Jiandong Duan
Keyword(s):  
Complex Network ◽  
Fractional Order ◽  
Control Method ◽  
Pinning Control ◽  
Projective Synchronization ◽  
Synchronization Control ◽  
Order Complex ◽  
Selection Algorithm ◽  
Feedback Control Method ◽  
Simulation Results

This paper presents an adaptive projective pinning control method for fractional-order complex network. First, based on theories of complex network and fractional calculus, some preliminaries of mathematics are given. Then, an analysis is conducted on the adaptive projective pinning control theory for fractional-order complex network. Based on the projective synchronization control method and the combined adaptive pinning feedback control method, suitable projection synchronization scale factor, adaptive feedback controller and the node selection algorithm are designed to illustrate the synchronization for fractional-order hyperchaotic complex network. Simulation results show that all nodes are stabilized to equilibrium point. Theoretical analysis and simulation results demonstrate that the designed adaptive projective pinning controllers are efficient.

Control of Discrete Time Chaotic Systems via Combination of Linear and Nonlinear Dynamic Programming

2014 ◽  
Vol 10 (1) ◽  
Author(s):  
Kaveh Merat ◽  
Jafar Abbaszadeh Chekan ◽  
Hassan Salarieh ◽  
Aria Alasty
Keyword(s):  
Discrete Time ◽  
Control Method ◽  
Controller Design ◽  
Chaotic Behavior ◽  
Noise Signal ◽  
Delayed Feedback Control ◽  
Optimal Controller ◽  
Clustering Method ◽  
Control Approach ◽  
Feedback Control Method

In this article by introducing and subsequently applying the Min–Max method, chaos has been suppressed in discrete time systems. By using this nonlinear technique, the chaotic behavior of Behrens–Feichtinger model is stabilized on its first and second-order unstable fixed points (UFP) in presence and absence of noise signal. In this step, a comparison has also been carried out among the proposed Min–Max controller and the Pyragas delayed feedback control method. Next, to reduce the computation required for controller design, the clustering method has been introduced as a quantization method in the Min–Max control approach. To improve the performance of the acquired controller through clustering method obtained with the Min–Max method, a linear optimal controller is also introduced and combined with the previously discussed nonlinear control law. The resultant combined controller has been applied on the Henon map and through comparison with both Pyragas controller, and the linear optimal controller alone, its advantages are discussed.

The Study of Optimal Fuzzy PID-Smith Control Based on Genetic Algorithm

2013 ◽  
Vol 313-314 ◽  
pp. 448-452
Author(s):  
Dian Ting Liu ◽  
Hai Xia Li
Keyword(s):  
Genetic Algorithm ◽  
Simulation Model ◽  
Control Method ◽  
Order System ◽  
Membership Functions ◽  
Fuzzy Pid ◽  
Improved Genetic Algorithm ◽  
Simulation Results ◽  
The Stability ◽  
Better Than

In this paper, the improved genetic algorithm is applied to optimize the quantization factors and the scaling factors of fuzzy control, and the optimized rule table and membership functions is obtained according to certain performances. Then a kind of optimal fuzzy PID-Smith control method based on genetic algorithm is proposed and its simulation model is built in this paper, a second-order system is simulated and analyzed. The results show that requirements of deterministic performances of the new control method are better than the conventional methods through the simulation results in the stability, rapidity and robustness.

Approximate Finite-Time Stable Control for Simple Interconnected Power Systems

2013 ◽  
Vol 846-847 ◽  
pp. 305-308
Author(s):  
Jian Li Zhao ◽  
Bao Feng Yan ◽  
Bo Chen
Keyword(s):  
Power Systems ◽  
Finite Time ◽  
Control Method ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Extended State ◽  
Interconnected Power Systems ◽  
Feedback Control Method ◽  
Simulation Results ◽  
Stable Control

Considering the simple interconnected power systems, the finite-time stable control problem is studied. A nonlinear feedback control method with dynamic active compensation is proposed, which makes the systems achieves approximately the finite-time stable control. Meantime, in order to solve the problem of system uncertainty and unmeasurable states, an extended state observer is designed. Simulation results show the effectiveness of the control method.

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.

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