Control of Chaotic Population Dynamics Using OPCL Method (original) (raw)
Analysis of chaotic behaviour in the population dynamics
Physica A: Statistical Mechanics and its Applications, 2001
Recently, we have shown that the Penna bitstring model for population senescence can be used to model cyclic or chaotic behaviours in population dynamics. In this paper, we analyse the attractor of the dynamics, through the calculation of the Lyapunov exponents. We obtained that the dynamics is characterized by the existence of some small exponents, which we relate to the existence of homeochaos, needed for the generation of stability and diversity in living systems.
Controlling Chaos In Ecology: From Deterministic to Individual-Based Models
Bulletin of mathematical …, 1999
The possibility of chaos control in biological systems has been stimulated by recent advances in the study of heart and brain tissue dynamics. More recently, some authors have conjectured that such a method might be applied to population dynamics and even play a nontrivial evolutionary role in ecology. In this paper we explore this idea by means of both mathematical and individual-based simulation models. Because of the intrinsic noise linked to individual behavior, controlling a noisy system becomes more difficult but, as shown here, it is a feasible task allowed to be experimentally tested.
Control, synchrony and the persistence of chaotic populations
Chaos, Solitons & Fractals, 2001
The existence of deterministic chaos has been reported to date for a small number of real ecosystems. However, advances in the quest for chaos may include the application of chaos control techniques. In this paper, we study a model system, that of vegetation–hares–lynx interactions, in order to show the effects that control may exert on the structure and dynamics of the populations at play. Control techniques work effectively not only under the deterministic description, but also under assumptions of demographic and environmental stochasticity and even using spatially oriented approaches. Finally, some outlines are drawn with respect to the ecological consequences of applying chaos control in real ecosystems.
Chaos Synchronization in Discrete-Time Dynamical Systems with Application in Population Dynamics
Journal of Applied Mathematics and Physics
Study of chaotic synchronization as a fundamental phenomenon in the nonlinear dynamical systems theory has been recently raised many interests in science, engineering, and technology. In this paper, we develop a new mathematical framework in study of chaotic synchronization of discrete-time dynamical systems. In the novel drive-response discrete-time dynamical system which has been coupled using convex link function, we introduce a synchronization threshold which passes that makes the drive-response system lose complete coupling and synchronized behaviors. We provide the application of this type of coupling in synchronized cycles of well-known Ricker model. This model displays a rich cascade of complex dynamics from stable fixed point and cascade of period-doubling bifurcation to chaos. We also numerically verify the effectiveness of the proposed scheme and demonstrate how this type of coupling makes this chaotic system and its corresponding coupled system starting from different initial conditions, quickly get synchronized.
Analysis and Simulation of Chaotic Systems
Applied Mathematical Sciences, 2000
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Computational Exploration of Chaotic Dynamics with an Associated Biological System
2014
Study of microbial populations has always been a topic of interest for researchers. This is because microorganisms have been of instrumental use in the various studies related to population dynamics, artificial biofuels etc. Comparatively short lifespan and availability are two big advantages they have which make them suitable for aforementioned studies. Their population dynamic helps us understand evolution. A lot can be revealed about resource consumption of a system by comparing it to the similar system where bacteria play the role of different factors in the system. Also, study of population dynamics of bacteria can reveal necessary initial conditions for the desired state of microbial population at some reference point in future. This makes it interesting for ecological and evolutionary disciplines. Chaos is a mathematical concept which characterizes behavior of dynamical systems that are highly sensitive to the initial conditions. Small differences in the initial conditions such as those due to rounding errors of values of initial parameters yield widely diverging outcomes for such dynamical systems. The way biological systems behave in nature, there is a reason to believe that they do indeed follow chaotic regime. Various mathematical models have been proposed to mimic biological systems in nature. We believe that models which follow chaotic regime represent the biological systems in better way and also are more efficient. We propose a new software tool which may help simulate the mathematical model at hand and provide view ii of different set of parameters which can keep the system in chaotic state. This may help researchers design better and efficient biological models or use existing models in better way.
Chaos, Solitons & Fractals, 2005
In recent years it has been increasingly recognized that noise and determinism may have comparable but different influences on population dynamics. However, no simple analysis methods have been introduced into ecology which can readily characterize those impacts. In this paper, we study a population model with strong periodicity and both with and without noise. The noise-free model generates both quasi-periodic and chaotic dynamics for certain parameter values. Due to the strong periodicity, however, the generated chaotic dynamics have not been satisfactorily described. The dynamics becomes even more complicated when there is noise. Characterizing the chaotic and stochastic dynamics in this model thus represents a challenging problem. Here we show how the chaotic dynamics can be readily characterized by the direct dynamical test for deterministic chaos developed by [Gao JB, Zheng ZM. Europhys. Lett. 1994;25:485] and how the influence of noise on quasi-periodic motions can be characterized as asymmetric diffusions wandering along the quasi-periodic orbit. It is hoped that the introduced methods will be useful in studying other population models as well as population time series obtained both in field and laboratory experiments.
The control of chaos: theory and applications
Physics Reports, 2000
Introduction 106 1.1. The control of chaos: exploiting the critical sensitivity to initial conditions to play with chaotic systems 106 1.2. From the Ott}Grebogi}Yorke ideas and technique to the other control methods 107 1.3. Targeting desirable states within chaotic attractors 108 1.4. The control of chaotic behaviors, and the communication with chaos 109 1.5. The experimental veri"cations of chaos control 110 1.6. Outline of the Report 110 2. The OGY method of controlling chaos 111 2.1. The basic idea 111 2.2. A one-dimensional example 111 2.3. Controlling chaos in two dimensions 114 2.4. Pole placement method of controlling chaos in high dimensions 121 2.5. Discussion 127 3. The adaptive method for control of chaos 128 3.1. The basic idea 128 3.2. The algorithm for adaptive chaos control 129 3.3. Application to high-dimensional systems 131 4. The problem of targeting 4.1. Targeting and controlling fractal basin boundaries 4.2. The adaptive targeting of chaos 5. Stabilizing desirable chaotic trajectories and application 5.1. Stabilizing desirable chaotic trajectories 5.2. The adaptive synchronization of chaos for secure communication 6. Experimental evidences and perspectives of chaos control 6.1. Introduction 6.2. Nonfeedback methods 6.3. Control of chaos with OGY method 6.4. Control of electronic circuits 6.5. Control of chemical chaos 6.6. Control of chaos in lasers and nonlinear optics 6.7. Control of chaos in #uids 6.8. Control of chaos in biological and biomechanical systems 6.9. Experimental control of chaos by time delay feedback 6.10. Other experiments
Chaos and chaos control in biology
Journal of Clinical Investigation, 1994
Chaos, in its mathematical sense, refers to irregular behavior that appears to be random, but is not. The recognition that an irregular behavior is chaotic, rather than random, signifies that a set of precise rules, rather than chance, governs the irregular behavior of the system. Therefore, if the system is sufficiently well understood, the irregular behavior can be predicted, eliminated, or controlled. Chaos theory has been applied very suc-
Algorithms for controlling chaotic motion: application for the BVP oscillator
Physica D-nonlinear Phenomena, 1993
The BVP oscillator is a biologically and physically important dynamical system exhibiting chaotic motion, phaselocking phenomenon and so on. In this paper we investigatc the controlling of chaos in this system both when periodic arid constant currents arc present. Wc use the various control algorithms and investigate their effectiveness. In particular wc study the controlling by the following mechanisms: (i) adaptive control algorithm: (it) weak periodic perturbations: (iii) Ott Grebogi Yorke method, (iv) weak fccdback control and (v) addition of noise. Also, we show the suppression of chaos by numerical models.
Chaotic dynamics of a nonlinear density dependent population model
Nonlinearity, 2004
We study the dynamics of an overcompensatory Leslie population model where the fertility rates decay exponentially with population size. We find a plethora of complicated dynamical behaviour, some of which has not been previously observed in population models and which may give rise to new paradigms in population biology and demography. We study the two-and three-dimensional models and find a large variety of complicated behaviour: all codimension 1 local bifurcations, period doubling cascades, attracting closed curves that bifurcate into strange attractors, multiple coexisting strange attractors with large basins (which cause an intrinsic lack of 'ergodicity'), crises that can cause a discontinuous large population swing, merging of attractors, phase locking and transient chaos. We find (and explain) two different bifurcation cascades transforming an attracting invariant closed curve into a strange attractor. We also find one-parameter families that exhibit most of these phenomena. We show that some of the more exotic phenomena arise from homoclinic tangencies.
From Chaos to Permanence Using Control Theory
2018
Work by Cushing et al. and Kot et al. demonstrate that chaotic behavior does occur in biological systems. We show that chaotic behavior can also be used to ensure the survival of the species involved in a system. We adopt the concept of permanence as a measure of survival and take advantage of present chaotic behavior to push a non-permanent system into permanence through a control algorithm. We apply the algorithm to a Lotka-Volterra type two-prey, one-predator model and a food chain model and demonstrate its effectiveness in taking advantage of chaotic behavior to achieve a desirable state for all species involved. In particular, we show that harvesting of the predator is a practical and effective control for insuring the thriving of all species in the system.
2020
In this work, we study hybrid projective combination synchronization scheme among identical chaotic generalized Lotka-Volterra three species biological systems using active control design. We consider here generalized Lotka-Volterra system containing two predators and one prey population existing in nature. An active control design is investigated which is essentially based on Lyapunov stability theory. The considered technique derives the global asymptotic stability using hybrid projective combination synchronization technique. In addition, the presented simulation outcomes and graphical results illustrate the validation of our proposed scheme. Prominently, both the analytical and computational results agree excellently. Comparisons versus others strategies exhibiting our proposed technique in generalized Lotka-Volterra system achieved asymptotic stability in a lesser time
A TWO-PARAMETER METHOD FOR CHAOS CONTROL AND TARGETING IN ONE-DIMENSIONAL MAPS
International Journal of Bifurcation and Chaos, 2013
We investigate a method of chaos control in which intervention is proportional to the difference between the current state and a fixed value. We prove that this method allows to stabilize the most usual one-dimensional maps used in discrete-time models of population dynamics about a globally stable positive equilibrium. From the point of view of targeting, this technique is very flexible, and we show how to choose the control parameter values to lead the system towards the desired target. Another important feature of this control scheme in the ecological context is that it can be designed to prevent the risk of extinction in models with the so-called Allee effect. We provide a useful geometrical interpretation, and give some examples to illustrate our theoretical results.
Physical Review Letters, 1990
We have achieved control of chaos in a physical system using the method of Ott, Grebogi, and Yorke [Phys. Rev. Lett. 64, 1196 (1990)]. The method requires only small time-dependent perturbations of a single-system parameter and does not require that one have model equations for the dynamics. We demonstrate the power of the method by controlling a chaotic system around unstable periodic orbits of order 1 and 2, switching between them at will.
Control of chaotic behaviour and prevention of extinction using constant proportional feedback
Nonlinear Analysis: Real World Applications, 2011
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.
A new approach to controlling chaotic systems
Physica D: Nonlinear Phenomena, 1998
Given a piecewise monotonic transformation r which is strongly transitive and preserves an invariant probability density function f, a construction is described which modifies r very slightly but which changes f significantly in order to possess desired properties. This construction permits control of the global long term behavior of chaotic dynamical systems.