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.

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 Bifurcation analysis and chaos control of a second-order exponential difference equation

Filomat ◽  
2019 ◽  
Vol 33 (15) ◽  
pp. 5003-5022 ◽  
Author(s):  
Q. Din ◽  
E.M. Elabbasy ◽  
A.A. Elsadany ◽  
S. Ibrahim
Keyword(s):  
Difference Equation ◽  
Chaos Control ◽  
Control Method ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Period Doubling ◽  
Second Order ◽  
Period Doubling Bifurcation ◽  
Positive Real ◽  
Second Order Difference Equation

The aim of this article is to study the local stability of equilibria, investigation related to the parametric conditions for transcritical bifurcation, period-doubling bifurcation and Neimark-Sacker bifurcation of the following second-order difference equation xn+1 = ?xn + ?xn-1 exp(-?xn-1) where the initial conditions x-1, x0 are the arbitrary positive real numbers and ?,? and ? are positive constants. Moreover, chaos control method is implemented for controlling chaotic behavior under the influence of Neimark-Sacker bifurcation and period-doubling bifurcation. Numerical simulations are provided to show effectiveness of theoretical discussion.

scholarly journals Experimental bifurcation control of a parametric pendulum

2015 ◽  
Vol 23 (14) ◽  
pp. 2256-2268 ◽  
Author(s):  
Aline S De Paula ◽  
Marcelo A Savi ◽  
Vahid Vaziri ◽  
Ekaterina Pavlovskaia ◽  
Marian Wiercigroch
Keyword(s):  
Control Method ◽  
Nonlinear Dynamic Analysis ◽  
Delayed Feedback Control ◽  
Bifurcation Diagrams ◽  
Good Qualitative Agreement ◽  
Wide Range ◽  
Parametric Pendulum ◽  
Feedback Control Method ◽  
Numerical Bifurcation ◽  
Time Delayed Feedback

The aim of the study is to maintain the desired period-1 rotation of the parametric pendulum over a wide range of the excitation parameters. Here the Time-Delayed Feedback control method is employed to suppress those bifurcations, which lead to loss of stability of the desired rotational motion. First, the nonlinear dynamic analysis is carried out numerically for the system without control. Specifically, bifurcation diagrams and basins of attractions are computed showing co-existence of oscillatory and rotary attractors. Then numerical bifurcation diagrams are experimentally validated for a typical set of the system parameters giving undesired bifurcations. Finally, the control has been implemented and investigated both numerically and experimentally showing a good qualitative agreement.

CONTROLLING CHAOS IN A CHAOTIC NEURON MODEL

2005 ◽  
Vol 15 (08) ◽  
pp. 2611-2621 ◽  
Author(s):  
WEI LIN ◽  
TIANPING CHEN
Keyword(s):  
Feedback Control ◽  
Periodic Orbits ◽  
Neuron Model ◽  
Control Method ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Unstable Periodic Orbits ◽  
Controlling Chaos ◽  
Feedback Control Method ◽  
Chaotic Neuron

In this paper we investigate several methods for controlling chaos in Aihara's chaotic neuron model. We first discuss the stability of exponential feedback control method for this model. To obviate predetermining the unstable periodic orbits of the system, two other methods are developed. We analyze why the conventional delayed feedback control method cannot be employed here, and then give a modified form for recursive delayed feedback control and apply it to control chaos in this model. To obtain high-periodic orbits more easily, a delayed exponential feedback control method is proposed, by which we can obtain different periodic orbits by changing parameters. Computer simulations show good control effects and robustness against noise.

scholarly journals Period-doubling bifurcation analysis and chaos control for load torque using FLC

2021 ◽  
Author(s):  
Eman Moustafa ◽  
Abdel-Azem Sobaih ◽  
Belal Abozalam ◽  
Amged Sayed A. Mahmoud
Keyword(s):  
Floquet Theory ◽  
Chaos Control ◽  
Fuzzy Logic Controller ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Parameter Variation ◽  
Period Doubling Bifurcation ◽  
Load Torque ◽  
Nonlinear Behaviors ◽  
Scientific Fields

AbstractChaotic phenomena are observed in several practical and scientific fields; however, the chaos is harmful to systems as they can lead them to be unstable. Consequently, the purpose of this study is to analyze the bifurcation of permanent magnet direct current (PMDC) motor and develop a controller that can suppress chaotic behavior resulted from parameter variation such as the loading effect. The nonlinear behaviors of PMDC motors were investigated by time-domain waveform, phase portrait, and Floquet theory. By varying the load torque, a period-doubling bifurcation appeared which in turn led to chaotic behavior in the system. So, a fuzzy logic controller and developing the Floquet theory techniques are applied to eliminate the bifurcation and the chaos effects. The controller is used to enhance the performance of the system by getting a faster response without overshoot or oscillation, moreover, tends to reduce the steady-state error while maintaining its stability. The simulation results emphasize that fuzzy control provides better performance than that obtained from the other controller.

ZERO-CROSS INSTANTANEOUS STATE SETTING FOR CONTROL OF A BIFURCATING H-BRIDGE INVERTER

2007 ◽  
Vol 17 (10) ◽  
pp. 3571-3575 ◽  
Author(s):  
SATOSHI AKATSU ◽  
HIROYUKI TORIKAI ◽  
TOSHIMICHI SAITO
Keyword(s):  
Pulse Width Modulation ◽  
Control Method ◽  
Period Doubling ◽  
Current Mode ◽  
Nonlinear Phenomena ◽  
Unstable Periodic Orbits ◽  
Bifurcation And Chaos ◽  
Zero Crossing ◽  
Modulation Signal ◽  
A Current

This paper studies stabilization of low-period unstable periodic orbits (UPOs) in a simplified model of a current mode H-bridge inverter. The switching of the inverter is controlled by pulse-width modulation signal depending on the sampled inductor current. The inverter can exhibit rich nonlinear phenomena including period doubling bifurcation and chaos. Our control method is realized by instantaneous opening of inductor at a zero-crossing moment of an objective UPO and can stabilize the UPO instantaneously as far as the UPO crosses zero in principle. Typical system operations can be confirmed by numerical experiments.

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.

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.

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.

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