"MIDDLE" PERIODIC ORBIT AND ITS APPLICATION TO CHAOS CONTROL

2002 ◽  
Vol 12 (08) ◽  
pp. 1869-1876
Author(s):  
LING YANG ◽  
ZENGRONG LIU ◽  
YONGAI ZHENG
Keyword(s):  
Periodic Orbit ◽  
Topological Entropy ◽  
Chaotic Attractor ◽  
Chaos Control ◽  
Initial Point ◽  
New Method ◽  
Controlling Chaos ◽  
The Given

In this paper, a new method, by which any point in a chaotic attractor can be guided to any target periodic orbit, is proposed. The "Middle" periodic orbit is used to lead an initial point in a chaotic attractor to a neighborhood of the target orbit, and then controlling chaos can be achieved by the improved OGY method. The time needed in the method using "Middle" periodic orbit is less than that of the OGY method, and is inversely proportional to the square of the topological entropy of the given map. An example is used to illustrate the results.

The Control of Chaos: Theoretical Schemes and Experimental Realizations

1998 ◽  
Vol 08 (08) ◽  
pp. 1643-1655 ◽  
Author(s):  
F. T. Arecchi ◽  
S. Boccaletti ◽  
M. Ciofini ◽  
R. Meucci ◽  
C. Grebogi
Keyword(s):  
Periodic Orbit ◽  
Chaotic Attractor ◽  
The State ◽  
Control Parameters ◽  
State Variables ◽  
Unstable Periodic Orbit ◽  
Control Of Chaos ◽  
Controlling Chaos ◽  
Feedback Techniques

Controlling chaos is a process wherein an unstable periodic orbit embedded in a chaotic attractor is stabilized by means of tiny perturbations of the system. These perturbations imply goal oriented feedback techniques which act either on the state variables of the system or on the control parameters. We review some theoretical schemes and experimental implementations for the control of chaos.

EXPERIMENTAL REALIZATION OF CONTROLLING CHAOS IN THE PERIODICALLY SWITCHED NONLINEAR CIRCUIT

2004 ◽  
Vol 14 (10) ◽  
pp. 3655-3660 ◽  
Author(s):  
TAKUJI KOUSAKA ◽  
YOSIHITO YASUHARA ◽  
TETSUSHI UETA ◽  
HIROSHI KAWAKAMI
Keyword(s):  
Periodic Orbit ◽  
Chaotic Attractor ◽  
Discrete System ◽  
Chaotic Behavior ◽  
Control Unit ◽  
Unstable Periodic Orbit ◽  
Nonlinear Circuit ◽  
Experimental Realization ◽  
Controlling Chaos ◽  
Window Comparator

This letter presents an experimental confirmation of controlling the chaotic behavior of a target unstable periodic orbit when the periodically switched nonlinear circuit has a chaotic attractor. The pole assignment for the corresponding discrete system derived from such a nonautonomous system via Poincaré mapping works effectively, and the control unit is easily realized by the window comparator, sample-hold circuits, and so on.

Chaos Control for a Fractional-Order Jerk System via Time Delay Feedback Controller and Mixed Controller

2021 ◽  
Vol 5 (4) ◽  
pp. 257
Author(s):  
Changjin Xu ◽  
Maoxin Liao ◽  
Peiluan Li ◽  
Lingyun Yao ◽  
Qiwen Qin ◽  
...  
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Chaos Control ◽  
Chaotic Behavior ◽  
Control Strategies ◽  
Feedback Controller ◽  
Research Approach ◽  
Controlling Chaos ◽  
The Stability ◽  
Jerk System

In this study, we propose a novel fractional-order Jerk system. Experiments show that, under some suitable parameters, the fractional-order Jerk system displays a chaotic phenomenon. In order to suppress the chaotic behavior of the fractional-order Jerk system, we design two control strategies. Firstly, we design an appropriate time delay feedback controller to suppress the chaos of the fractional-order Jerk system. The delay-independent stability and bifurcation conditions are established. Secondly, we design a suitable mixed controller, which includes a time delay feedback controller and a fractional-order PDσ controller, to eliminate the chaos of the fractional-order Jerk system. The sufficient condition ensuring the stability and the creation of Hopf bifurcation for the fractional-order controlled Jerk system is derived. Finally, computer simulations are executed to verify the feasibility of the designed controllers. The derived results of this study are absolutely new and possess potential application value in controlling chaos in physics. Moreover, the research approach also enriches the chaos control theory of fractional-order dynamical system.

Periodic Perturbation Method for Controlling Chaos for a Positive Output DC-DC Luo Converter

2017 ◽  
Vol 8 (2) ◽  
pp. 775 ◽  
Author(s):  
P. Balamurugan ◽  
A. Kavitha ◽  
P. Sanjeevikumar ◽  
J.L. Febin Daya ◽  
Tole Sutikno
Keyword(s):  
Control Strategy ◽  
Chaotic Attractor ◽  
Current Mode ◽  
Chaotic Regime ◽  
Periodic Perturbation ◽  
Control Technique ◽  
Controlling Chaos ◽  
Stable Period ◽  
Feedback Method ◽  
A Current

<p>A simple, non-feedback method of controlling chaos is implemented for a DC-DC converter. The weak periodic perturbation (WPP) is the control technique applied to stabilize an unstable orbit in a current-mode controlled Positive Output Luo (POL) DC-DC converter operating in a chaotic regime. With WPP, the operation of the converter is limited to stable period-1 orbit that exists in the original chaotic attractor. The proposed control strategy is implemented using simulations and the results are verified with hardware setup. The experimental results of the converter with WPP control are presented which shows the effectiveness of the control strategy.</p>

scholarly journals Stability of Switched Server Systems with Constraints on Service-Time and Capacity of Buffers

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Li Wang ◽  
Zhonghe He ◽  
Chi Zhang
Keyword(s):  
Periodic Orbit ◽  
Service Time ◽  
Buffer Capacity ◽  
Time Factors ◽  
Upper Bounds ◽  
Finite Buffer ◽  
Lower And Upper Bounds ◽  
Upper Limit ◽  
Server Systems ◽  
The Given

The execution of emptying policy ensures the convergence of any solution to the system to a unique periodic orbit, which does not impose constraints on service-time and capacity of buffers. Motivated by these problems, in this paper, the service-time-limited policy is first proposed based on the information resulted from the periodic orbit under emptying policy, which imposes lower and upper bounds on emptying time for the queue in each buffer, by introducing lower-limit and upper-limit service-time factors. Furthermore, the execution of service-time-limited policy in the case of finite buffer capacity is considered. Moreover, the notion of feasibility of states under service-time-limited policy is introduced and then the checking condition for feasibility of states is given; that is, the solution does not exceed the buffer capacity within the first cycle of the server. At last, a sufficient condition for determining upper-limit service-time factors ensuring that the given state is feasible is given.

An Improved Method for Gas Lift Allocation Optimization

1995 ◽  
Vol 117 (2) ◽  
pp. 87-92 ◽  
Author(s):  
N. Nishikiori ◽  
R. A. Redner ◽  
D. R. Doty ◽  
Z. Schmidt
Keyword(s):  
Optimization Technique ◽  
Gas Injection ◽  
Initial Point ◽  
Optimization Method ◽  
New Method ◽  
Superior Performance ◽  
Total Oil ◽  
Quasi Newton ◽  
Gas Lift ◽  
Injection Rates

A new method for finding the optimum gas injection rates for a group of continuous gas lift wells to maximize the total oil production rate is established. The new method uses a quasi-Newton nonlinear optimization technique which is incorporated with the gradient projection method. The method is capable of accommodating restrictions to the gas injection rates. The only requirement for fast convergence is that a reasonable estimate of the gas injection rates must be supplied as an initial point to the optimization method. A method of estimating the gas injection rates is developed for that purpose. A computer program is developed capable of implementing the new optimization method as well as generating the initial estimate of the gas injection rates. This program is then successfully tested on field data under both unlimited and limited gas supply. The new optimization technique demonstrates superior performance, faster convergence, and greater application.

DYNAMICS OF THE MUTHUSWAMY–CHUA SYSTEM

2013 ◽  
Vol 23 (08) ◽  
pp. 1350136 ◽  
Author(s):  
YUANFAN ZHANG ◽  
XIANG ZHANG
Keyword(s):  
Periodic Orbit ◽  
Periodic Orbits ◽  
Chaotic Attractor ◽  
Electronic Circuit ◽  
Small Perturbations ◽  
Chaotic Phenomena ◽  
Invariant Surfaces

The Muthuswamy–Chua system [Formula: see text] describes the simplest electronic circuit which can have chaotic phenomena. In this paper, we first prove the existence of three families of consecutive periodic orbits of the system when α = 0, two of which are located on consecutive invariant surfaces and form two invariant topological cylinders. Then we prove that for α > 0 if the system has a periodic orbit or a chaotic attractor, it must intersect both of the planes z = 0 and z = -1 infinitely many times as t tends to infinity. As a byproduct, we get an example of unstable invariant topological cylinders which are not normally hyperbolic and which are also destroyed under small perturbations.

CHAOS CONTROL IMPLEMENTATION BY INTERRUPTED ELECTRIC CIRCUIT WITH SWITCHING DELAY

2009 ◽  
Vol 19 (07) ◽  
pp. 2359-2362
Author(s):  
TAKUJI KOUSAKA ◽  
TETSUSHI UETA ◽  
YUE MA
Keyword(s):  
Periodic Orbit ◽  
Chaos Control ◽  
Electric Circuit ◽  
Unstable Periodic Orbit ◽  
Chaotic Circuit ◽  
Return Map ◽  
Switching Delay ◽  
Suppression Of Chaos ◽  
Control Implementation

We have demonstrated that the chaotic circuit with a switching delay is modeled by a return map, and a controller for the suppression of chaos is proposed. A circuit representing a controller stabilizing a period-1 unstable periodic orbit in an interrupted electric circuit with a certain switching delay is also discussed.

CHAOS IN NONAUTONOMOUS DISCRETE DYNAMICAL SYSTEMS APPROACHED BY THEIR INDUCED SYSTEMS

2012 ◽  
Vol 22 (11) ◽  
pp. 1250284 ◽  
Author(s):  
YUMING SHI
Keyword(s):  
Discrete Dynamical System ◽  
Sufficient Conditions ◽  
Initial Point ◽  
Original System ◽  
Discrete Dynamical Systems ◽  
Strong Sense ◽  
Nonautonomous Systems ◽  
Original Order ◽  
Dynamical Behaviors ◽  
The Given

A nonautonomous discrete dynamical system is generated by a given sequence of maps. Its induced system is introduced. It is generated by a sequence of maps that are partial compositions of the given sequence of maps in the original order so that every orbit of the induced system is a part of an orbit of the original system starting from the same initial point. Some close relationships between chaotic dynamical behaviors of the original system and its induced systems are given, including chaos in the (strong) sense of Li–Yorke and Wiggins. Under some conditions, chaos in the (strong) sense of Li–Yorke of the original system and its induced systems is equivalent. By applying these relationships, several criteria of chaos are established and some sufficient conditions for no chaos are given for nonautonomous systems.

Global Bifurcation Approximation in Controlling Chaotic Systems

1998 ◽  
Vol 08 (05) ◽  
pp. 1013-1023
Author(s):  
Byoung-Cheon Lee ◽  
Bong-Gyun Kim ◽  
Bo-Hyeun Wang
Keyword(s):  
Feedback Control ◽  
Periodic Orbit ◽  
Periodic Orbits ◽  
Chaotic Attractor ◽  
Global Bifurcation ◽  
Good Control ◽  
Hysteresis Phenomenon ◽  
Unstable Periodic Orbits ◽  
Tracking Method ◽  
Adaptive Tracking

In our previous research [Lee et al., 1995], we demonstrated that return map control and adaptive tracking method can be used together to locate, stabilize and track unstable periodic orbits (UPO) automatically. Our adaptive tracking method is based on the control bifurcation (CB) phenomenon which is another route to chaos generated by feedback control. Along the CB route, there are numerous driven periodic orbits (DPOs), and they can be good control targets if small system modification is allowed. In this paper, we introduce a new control concept of global bifurcation approximation (GBA) which is quite different from the traditional local linear approximation (LLA). Based on this approach, we also demonstrate that chaotic attractor can be induced from a periodic orbit. If feedback control is applied along the direction to chaos, small erratic fluctuations of a periodic orbit is magnified and the chaotic attractor is induced. One of the special features of CB is the existence of irreversible orbit (IO) which is generated at the strong extreme of feedback control and has irreversible property. We show that IO induces a hysteresis phenomenon in CB, and we discuss how to keep away from IO.

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