Self-modulation suppression in the delayed-feedback klystron-type oscillator via the chaos control method

2011 ◽  
Vol 56 (6) ◽  
pp. 690-698 ◽  
Author(s):  
N. M. Ryskin ◽  
O. S. Khavroshin
Keyword(s):  
Chaos Control ◽  
Control Method ◽  
Delayed Feedback

PERIODIC RESPONSE TO EXTERNAL STIMULATION OF A CHAOTIC NEURAL NETWORK WITH DELAYED FEEDBACK

1999 ◽  
Vol 09 (04) ◽  
pp. 713-722 ◽  
Author(s):  
ALBAN PUI MAN TSUI ◽  
ANTONIA J. JONES
Keyword(s):  
Neural Network ◽  
Chaos Control ◽  
Control Method ◽  
Original System ◽  
Neural System ◽  
Delayed Feedback ◽  
Input Stimulus ◽  
Biologically Inspired ◽  
External Stimulation ◽  
Different Types

We construct a feedforward neural network so that when the outputs are fed back into the inputs and the system is iterated it behaves chaotically. We call this the "rest state". Suppose now that an input stimulus is added to one or more inputs. Following a biologically inspired model suggested by Freeman [1991], under these conditions we should want the behavior of the network to stabilize into an unstable periodic orbit of the original system. We call this the "retrieval behavior" since it is analogous to the act of recognition. Standard methods of chaos control, such as OGY for example, used to elicit the retrieval behavior would be inappropriate, since such methods involve calculations external to the system being controlled and can be considered unlikely in a biological neural network. Using a chaos control method originally suggested by Pyragas [1992] we show that retrieval behavior can occur as a result of delayed feedback and examine the variety of the responses that arise under different types of stimuli and under noise. This artificial neural system has a strong dynamical parallel to Freeman's observed biological phenomenon.

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.

scholarly journals Synchronization and Anti-Synchronization of Two Identical Hyperchaotic Systems Based on Active Backstepping Design

2011 ◽  
pp. 117-122
Author(s):  
Atefeh Saedian ◽  
Hassan Zarabadipoor
Keyword(s):  
Numerical Simulations ◽  
Active Control ◽  
Chaos Control ◽  
Control Method ◽  
Design Method ◽  
Backstepping Design ◽  
Backstepping Technique ◽  
Control Approach ◽  
Hyperchaotic Systems

This paper presents an active backstepping design method for synchronization and anti-synchronization of two identical hyperchaotic Chen systems. The proposed control method, combining backstepping design and active control approach, extends the application of backstepping technique in chaos control. Based on this method, different combinations of controllers can be designed to meet the needs of different applications. Numerical simulations are shown to verify the results.

EXPERIMENTAL VERIFICATION OF PYRAGAS’S CHAOS CONTROL METHOD APPLIED TO CHUA’S CIRCUIT

1994 ◽  
Vol 04 (06) ◽  
pp. 1703-1706 ◽  
Author(s):  
P. CELKA
Keyword(s):  
Periodic Orbits ◽  
Experimental Verification ◽  
Chaos Control ◽  
Control Method ◽  
Experimental Results ◽  
Experimental Setup ◽  
Chua’S Circuit ◽  
Unstable Periodic Orbits ◽  
Chua's Circuit

We have built an experimental setup to apply Pyragas’s [1992, 1993] control method in order to stabilize unstable periodic orbits (UPO) in Chua’s circuit. We have been able to control low period UPO embedded in the double scroll attractor. However, experimental results show that the control method is useful under some restrictions we will discuss.

Intervention Time in Target-Oriented Chaos Control

2021 ◽  
Vol 31 (09) ◽  
pp. 2150134
Author(s):  
Juan Segura
Keyword(s):  
Discrete Time ◽  
Chaos Control ◽  
Control Method ◽  
Single Species ◽  
Positive Equilibrium ◽  
Population Stability ◽  
Determine Parameter ◽  
And Control ◽  
Parameter Values ◽  
Proportional Feedback

The timing of interventions plays a central role in managing and exploiting biological populations. However, few studies in the literature have addressed its effect on population stability. The Seno equation is a discrete-time equation that describes the dynamics of single-species populations harvested according to the proportional feedback method at any moment between two consecutive censuses. Here we study a discrete-time equation that generalizes the Seno equation by considering the management and exploitation of populations through the target-oriented chaos control method. We investigate the combined effect of timing, targeting, and control on population stability, focusing on global stability. We prove that high enough control values create a positive equilibrium that attracts all positive solutions. We also prove that it is possible to determine parameter values to stabilize the controlled populations at any preset population size. Finally, we investigate the parameter combinations for which the management and exploitation are optimized in different scenarios.

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.

Bifurcations and chaos control in a discrete-time biological model

2020 ◽  
Vol 13 (04) ◽  
pp. 2050022 ◽  
Author(s):  
A. Q. Khan ◽  
T. Khalique
Keyword(s):  
Discrete Time ◽  
Chaos Control ◽  
Control Method ◽  
Complex Dynamics ◽  
Small Neighborhood ◽  
Positive Equilibrium ◽  
Global Dynamics ◽  
Flip Bifurcation ◽  
Time Model ◽  
Predator Prey Model

In this paper, bifurcations and chaos control in a discrete-time Lotka–Volterra predator–prey model have been studied in quadrant-[Formula: see text]. It is shown that for all parametric values, model has boundary equilibria: [Formula: see text], and the unique positive equilibrium point: [Formula: see text] if [Formula: see text]. By Linearization method, we explored the local dynamics along with different topological classifications about equilibria. We also explored the boundedness of positive solution, global dynamics, and existence of prime-period and periodic points of the model. It is explored that flip bifurcation occurs about boundary equilibria: [Formula: see text], and also there exists a flip bifurcation when parameters of the discrete-time model vary in a small neighborhood of [Formula: see text]. Further, it is also explored that about [Formula: see text] the model undergoes a N–S bifurcation, and meanwhile a stable close invariant curves appears. From the perspective of biology, these curves imply that between predator and prey populations, there exist periodic or quasi-periodic oscillations. Some simulations are presented to illustrate not only main results but also reveals the complex dynamics such as the orbits of period-2,3,13,15,17 and 23. The Maximum Lyapunov exponents as well as fractal dimension are computed numerically to justify the chaotic behaviors in the model. Finally, feedback control method is applied to stabilize chaos existing in the model.

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