Control Of Chaotic Behavior Research Articles

Discrete-Time Predator-Prey Interaction with Selective Harvesting and Predator Self-Limitation

Selective harvesting plays an important role on the dynamics of predator-prey interaction. On the other hand, the effect of predator self-limitation contributes remarkably to the stabilization of exploitative interactions. Keeping in view the selective harvesting and predator self-limitation, a discrete-time predator-prey model is discussed. Existence of fixed points and their local dynamics is explored for the proposed discrete-time model. Explicit principles of Neimark–Sacker bifurcation and period-doubling bifurcation are used for discussion related to bifurcation analysis in the discrete-time predator-prey system. The control of chaotic behavior is discussed with the help of methods related to state feedback control and parameter perturbation. At the end, some numerical examples are presented for verification and illustration of theoretical findings.

Analyses and Control of Chaotic Behavior in DC-DC Converters

In this study the nonlinear behavior of a buck converter was simulated and the responses of Phases 1 and 2 and the chaotic phase were investigated using changes of input voltage. After a dynamic system model had been acquired using basic electronic circuit theory, Matlab and Pspice simulations were used to study system inductance, resistance, and capacitance. The characteristic changes of input voltage, and phase plane traces from simulation and experiments showed nonlinear behavior in Phases 1 and 2, as well as a chaotic phase. PID control and Integral Absolute Error (IAE) were used as adaption coefficients to control chaotic behavior, and particle swarm optimization (PSO) and the genetic algorithm were used to find the optimal gain parameters for the PID controller. Simulation results showed that the control of chaotic phenomena could be achieved and errors were close to zero. Fuzzy control was also used effectively to prevent chaos. The experimental results also showed nonlinear behavior from Phases 1 and 2 as well as the chaotic phase. Laboratory experiments conducted using both PID and fuzzy control echoed the simulation results. The fuzzy control results were somewhat better than those obtained with PID.

Robust controlling of chaotic behavior in supply chain networks

The supply chain network is a complex nonlinear system that may have a chaotic behavior. This network involves multiple entities that cooperate to meet customers demand and control network inventory. Although there is a large body of research on measurement of chaos in the supply chain, no proper method has been proposed to control its chaotic behavior. Moreover, the dynamic equations used in the supply chain ignore many factors that affect this chaotic behavior. This paper offers a more comprehensive modeling, analysis, and control of chaotic behavior in the supply chain. A supply chain network with a centralized decision-making structure is modeled. This model has a control center that determines the order of entities and controls their inventories based on customer demand. There is a time-varying delay in the supply chain network, which is equal to the maximum delay between entities. Robust control method with linear matrix inequality technique is used to control the chaotic behavior. Using this technique, decision parameters are determined in such a way as to stabilize network behavior.

Robust H$\infty $ control for chaotic supply chain networks

A supply chain network (SCN) is a complex nonlinear system involving multiple entities. The policy of each entity in decision-making and the uncertainties of demand and supply (or production) significantly affect the complexity of its behavior. Although several studies have presented information about the measurement of chaos in the supply chain, there has not been an appropriate way to control the chaos in it. In this paper, the chaos control problem is considered for a SCN with a time-varying delay between its entities. The innovation of this paper is the more comprehensive modeling, analysis, and control of chaotic behavior in the system. The proposed model has a control center to determine the orders of entities and control their inventories. Customer demand is modeled as an unknown exogenous disturbance. A robust H$\infty $ control method is designed to control its chaotic behavior in terms of a certain linear matrix inequality technique that can be readily solved using the MATLAB LMI toolbox. By using this technique and calculating the maximum Lyapunov exponent, decision parameters are determined in such a way that the behavior of the SCN is stable.

Analysis and control of chaotic behavior in boost converter by ramp compensation based on Lyapunov exponents assignment: theoretical and experimental investigation

Nonlinear analysis of complex dynamics displayed by current mode dc–dc converter and idea of Lyapunov exponents assignment by ramp compensator in order to control chaotic behavior is proposed in this article. A discrete-time iterative nonlinear mapping model is derived. The occurrence of the complex behaviors of bifurcation and chaos generated by varying the circuit parameters are investigated through numerical analysis and software implementation of the circuit. Next, in order to control bifurcation and chaos in these converters, the ramp compensation method is used. By inserting the ramp compensation parameter in the dynamical equations of the system, these complex behaviors are examined theoretically and numerically as well. It is proved that through this method, the stable period-one operation of the converter can be extended. By evaluating the Lyapunov exponents (LEs) of the system, the impact of the slope on the location of LEs are determined analytically. This leads to a design methodology for control of chaos in this converter based on LEs assignment in desired values by proper selection of compensator slope. By developing an experimental set up, practical results are obtained to confirm the theoretical analysis and simulations.

State space reconstruction applied to a multiparameter chaos control method

The idea of the chaos control is the stabilization of unstable periodic orbits (UPOs) embedded in chaotic attractors. The OGY method achieves system stabilization by using small perturbations promoted in the neighborhood of the desired orbit when the trajectory crosses a Poincare section. A generalization of this method considers multiple actuations of parameters and sections, known as semi-continuous multiparameter method. This paper investigates the state space reconstruction applied to this general method, allowing chaotic behavior control of systems with non-observable states using multiple control parameters from time series analysis, avoiding the use of governing equations. As an application of the proposed multiparameter general formulation it is presented an uncoupled approach where the control parameters do not influence the system dynamics when they are not active. This method is applied to control chaos in a nonlinear pendulum using delay coordinates to perform state space reconstruction. Results show that the proposed procedure can be applied together with delay coordinates providing UPO stabilization.

Bifurcation and Chaos in Delayed Cellular Neural Network Model

This paper deals with control of chaotic behavior of a delayed Cellular Neural Network (DCNN) model which is a one-dimensional regular array of four cells with continuous activation function. We investigate different dynamical behaviors including limit cycle, torus, and chaos for different range of weight parameters of the system. Regarding synaptic weight as parameter, Hopf bifurcations are obtained in the system without delay. In the delayed model condition for the Global asymptotic stability of the equilibrium point is presented. Numerical simulation and results are given to show the role of delay in chaos control of the CNNs.

Control of Chaotic Behaviour in Parallel-Connected DC-DC Boost Converters

Chaos control means to design a controller that is able to eliminating the chaos behaviour of nonlinear systems that experiencing such phenomenon. In this paper, a delayed feedback control mode is presented. The paper describes the control of the bifurcation behaviour of a modular peak current-mode controlled DC-DC boost converter which is used to provide an interface between energy storage batteries and photovoltaic (PV) arrays renewable energy sources. The parallel-input/parallel-output converter comprises two identical boost circuits and operates in the continuous-current conduction mode. A comparison is made between waveforms obtained from a MATLAB/SIMULINK model for open-loop converter and the controlled one. The study shows the effectiveness of the designed delayed feedback control mode.

Control of chaos in positive output Luo converter using slope compensation method

This paper illustrates the control of chaotic behaviour in positive output Luo converter by slope compensation method. Bifurcation analysis is carried out in the discrete domain for a current controlled Luo converter operating in the continuous conduction mode. As the reference current is varied, periodic 1 orbit undergoes a flip bifurcation, periodic doubling and finally enters into chaotic regime. Variable ramp compensation technique is proposed to dynamically adjust the slope of the inductor current such that the upper bound of Iref is increased thereby widening the operating range. An iterative function that describes the dynamics of the inductor current with and without variable ramp compensation and the equivalent criteria for bifurcation-free operation is derived. A computer simulation using MATLAB/Simulink confirms the predicted bifurcations. The simulated results are validated through hardware implementation.

Control of chaotic behaviour and prevention of extinction using constant proportional feedback

We study a strategy to control the dynamics of one dimensional discrete maps known as the proportional feedback control method. We completely characterize the maps for which it is possible to stabilize the unstable or even chaotic dynamics towards an asymptotically stable equilibrium employing this method. Additionally, under conditions commonly assumed in modelling population dynamics, we show that the strategy drives the system to the optimal situation from a practical point of view, that is, to a global stable equilibrium since in that case the basin of attraction covers all the possible initial conditions. We also show that in some situations the strategy can be used to prevent the extinction of the population when controlling some models with the Allee effect.

Low-dimensional chaos and wave turbulence in plasmas

We investigated drift-wave turbulence in the plasma edge of a small tokamak by considering solutions of the Hasegawa-Mima equation involving three interacting modes in Fourier space. The resulting low-dimensional dynamics presented periodic as well as chaotic evolution of the Fourier-mode amplitudes, and we performed the control of chaotic behaviour through the application of a fourth resonant wave of small amplitude.

CONTROLLING CHAOS IN HIGHER-ORDER DYNAMICAL SYSTEMS

In this paper, we investigate a continuous extension of the Ott, Grebogi and Yorke control method [Ott et al., 1990]. This extension allows the control of chaotic behavior in higher-order dynamical systems. To begin with, studying the so-called Poincaré Sections (PS) enables determining fixed points and the effect of small changes in the control parameter on the system trajectory. Introduction of a stabilizer parameter in the control law keeps the dynamical properties and maintains them on a cyclic trajectory. The effectiveness of the proposed method is tested by numerical examples on the two typical Chen and Chua chaotic systems.

Controlling chaos in a model for an electrochemical oscillator using a map-based algorithm

We report the stabilisation of unstable periodic orbits in a numerical model for an electrochemical oscillator. Since the system is highly dissipative, the chaotic attractor has a dimension slightly greater than two, and the system can be described by a one-dimensional return map. Control of chaotic behavior in such systems can be achieved using a simple map-based control strategy.