scholarly journals A TWO-PARAMETER METHOD FOR CHAOS CONTROL AND TARGETING IN ONE-DIMENSIONAL MAPS

2013 ◽  
Vol 23 (01) ◽  
pp. 1350003 ◽  
Author(s):  
DANIEL FRANCO ◽  
EDUARDO LIZ
Keyword(s):  
Chaos Control ◽  
Point Of View ◽  
Positive Equilibrium ◽  
Parameter Method ◽  
One Dimensional ◽  
Current State ◽  
Control Scheme ◽  
The Difference ◽  
One Dimensional Maps ◽  
Parameter Values

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.

STABILIZATION OF CHAOTIC DYNAMICS OF ONE-DIMENSIONAL MAPS BY A CYCLIC PARAMETRIC TRANSFORMATION

1996 ◽  
Vol 06 (04) ◽  
pp. 725-735 ◽  
Author(s):  
ALEXANDER Yu. LOSKUTOV ◽  
VALERY M. TERESHKO ◽  
KONSTANTIN A. VASILIEV
Keyword(s):  
Periodic Orbits ◽  
Chaotic Dynamics ◽  
Chaotic Maps ◽  
Logistic Map ◽  
Exponential Map ◽  
One Dimensional ◽  
Stable Periodic ◽  
One Dimensional Maps ◽  
Parameter Values ◽  
Parametric Transformation

We consider one-dimensional maps, the logistic map and an exponential map, in those sets of parameter values which correspond to their chaotic dynamics. It is proven that such dynamics may be stabilized by a certain cyclic parametric transformation operating strictly within the chaotic set. The stabilization is a result of the creation of stable periodic orbits in the initially chaotic maps. The period of these stable orbits is a multiple of the period of the cyclic transformation. It is shown that stabilized behavior cannot be destroyed by a weak noise smearing of the required parameter values. The regions where the behavior stabilization takes place are numerically estimated. Periods of the created stabile periodic orbits are calculated.

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 Stability and Anti-Chaos Control of Discrete Quadratic Maps

2021 ◽  
pp. 1675-1685
Author(s):  
Sarbast H. Mikaee ◽  
George Maria Selvam ◽  
Vignesh D. Shanmugam ◽  
Bewar Beshay
Keyword(s):  
Dynamical System ◽  
Bifurcation Theory ◽  
Chaos Control ◽  
Order System ◽  
System Of Equations ◽  
Quadratic Maps ◽  
First Order ◽  
Current State ◽  
Chaotic Nature ◽  
Parameter Values

A dynamical system describes the consequence of the current state of an event or particle in future. The models expressed by functions in the dynamical systems are more often deterministic, but these functions might also be stochastic in some cases. The prediction of the system's behavior in future is studied with the analytical solution of the implicit relations (Differential, Difference equations) and simulations. A discrete-time first order system of equations with quadratic nonlinearity is considered for study in this work. Classical approach of stability analysis using Jury's condition is employed to analyze the system's stability. The chaotic nature of the dynamical system is illustrated by the bifurcation theory. The enhancement of chaos is performed using Cosine Chaotification Technique (CCT). Simulations are carried out for different parameter values.

Certain Problems with the Application of Stochastic Diffusion Processes for the Description of Chemical Engineering Phenomena. Stochastic Model of Isothermal Continuous Flow Chemical Reactor

1994 ◽  
Vol 59 (8) ◽  
pp. 1772-1787
Author(s):  
Vladimír Kudrna ◽  
Libor Vejmola ◽  
Pavel Hasal
Keyword(s):  
Continuous Flow ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Chemical Reactor ◽  
Point Of View ◽  
General Point ◽  
Stochastic Description ◽  
One Dimensional ◽  
Reactor Operating ◽  
Parameter Values

A model of an isothermal one-dimensional continuous flow chemical reactor operating at the steady state was derived using a stochastic description of motion of the reacting molecules. The model enables evaluation of the conversion of the reacting components. At the limiting parameter values the model yields results identical to those of the simplified models conventionally used in chemical reactor engineering. The model also enables the applicability of Danckwerts' boundary conditions to be assessed from a more general point of view.

scholarly journals Iteration of piecewise linear maps on an interval

1981 ◽  
Vol 24 (3) ◽  
pp. 433-451 ◽  
Author(s):  
James B. McGuire ◽  
Colin J. Thompson
Keyword(s):  
Invariant Measures ◽  
Piecewise Linear ◽  
Point Of View ◽  
Complete Analysis ◽  
Functional Composition ◽  
One Dimensional ◽  
Linear Maps ◽  
Piecewise Linear Maps ◽  
Parameter Values ◽  
Dense Set

A complete analysis is given of the iterative properties of two piece-piecewise linear maps on an interval, from the point of view of a doubling transformation obtained by functional composition and rescaling. We show how invariant measures may be constructed for such maps and that parameter values where this may be done form a dense set in a one-dimensional subset of parameter space.

scholarly journals Victimological Aspects of the Development of Restorative Mediation Practices in a Multicultural Society: Problems, Needs, Development Prospects

2020 ◽  
pp. 158-166
Author(s):  
Olga O. Andronnikova ◽  
Olga E. Radzikhovskaya
Keyword(s):  
Point Of View ◽  
Russian Society ◽  
Cultural Patterns ◽  
Multicultural Society ◽  
Multicultural Environment ◽  
Current State ◽  
The Difference ◽  
And Migration ◽  
Development Prospects

The article discusses the difference between victimization tension in a multicultural and multicultural society. The authors determine a characteristic of the current state of development of society and indicate the consequences of transition, globalization and geopolitical changes. The problems of education arising in a multicultural environment are highlighted. The analysis of the effectiveness of using the restorative approach of school mediation services in Russia and abroad is presented. The article provides an analysis of victimization of Russian society, which determines the main zones of victimization arising as a result of geopolitical and migration processes. Six main territories that are vulnerable from the point of view of the emergence of a multicultural environment were identified. Communities with victim motivational and fundamental characteristics aimed at preserving identity without the exchange of cultural patterns are described. It is indicated that for educational purposes in territories with multicultural tendencies, the educational type of mediation is the most interesting

The e3value Ontology for Value Networks: Current State and Future Directions

2016 ◽  
Vol 30 (2) ◽  
pp. 113-133 ◽  
Author(s):  
Hans Weigand
Keyword(s):  
Business Models ◽  
Point Of View ◽  
Model Quality ◽  
Economic Point ◽  
Exchange Value ◽  
Current State ◽  
Graphical Tool ◽  
New Business ◽  
Value Modeling ◽  
The Difference

ABSTRACT Meeting changing customer demands and business opportunities in a connected world makes it necessary for organizations to constantly innovate by means of value-creating collaborations. The goal of value modeling is to support the exploration of new business models from an economic point of view. The e3value approach to value modeling is based on an explicit ontology and supported by a graphical tool. This paper provides a structured overview and evaluation of e3value, and discusses two important issues. The first issue concerns the difference between a value co-creation perspective and an exchange value perspective. It shows that with some extensions, e3value can support both. The second issue is model quality. It argues that an ontology is not complete without model quality features and, as far as e3value is concerned, proposes to use the notion of “value cycle” as a soundness feature and as a replacement of the scenario concept.

scholarly journals Synchronization in ensembles of coupled maps with a major element

2005 ◽  
Vol 2005 (3) ◽  
pp. 239-255 ◽  
Author(s):  
Iryna Omelchenko ◽  
Yuri Maistrenko ◽  
Erik Mosekilde
Keyword(s):  
Chaotic Maps ◽  
Major Element ◽  
The Other ◽  
Parameter Mismatch ◽  
Partial Synchronization ◽  
One Dimensional ◽  
Coupled Maps ◽  
One Dimensional Maps ◽  
Parameter Values ◽  
Two Populations

The paper investigates the conditions for full and partial synchronization in systems of coupled chaotic maps that include the presence of a major element, that is, an element that interacts with all the other elements of the system. We consider a system which consists of two globally coupled populations of one-dimensional maps that interact via a major element. The presence of this element can induce synchronization in both of the globally coupled populations even though they operate in different states. If a parameter mismatch is introduced between two populations of uncoupled maps, the presence of a major element is found to provide for the existence of states in which peripheral elements with different parameter values display similar dynamics.

scholarly journals Competition among Predators and Allee Effect on Prey, Their Influence on a Gause-Type Predation Model

2019 ◽  
Vol 2019 ◽  
pp. 1-19 ◽  
Author(s):  
Eduardo González-Olivares ◽  
Javier Cabrera-Villegas ◽  
Fernando Córdova-Lepe ◽  
Alejandro Rojas-Palma
Keyword(s):  
Allee Effect ◽  
Equilibrium Points ◽  
Point Of View ◽  
Volterra Model ◽  
Positive Equilibrium ◽  
Boundedness Of Solutions ◽  
Separatrix Curve ◽  
Strong Allee Effect ◽  
The Difference ◽  
The Relationship

Interference or competition among predators (CAP) has often been ruled out in depredation models, although there are varied mathematical forms to describe and incorporate it into this interaction. In this work, we present the most known of these descriptions and one of them will be used in a modified Volterra model. Moreover, of this ecological phenomenon, a simple and strong Allee effect affecting the prey population will be considered in the relationship. An important feature of the new model is to have until two positive equilibrium points, to the difference with the Volterra model (without Allee effect); hence different and interesting dynamic situations appear in the system. Conditions for the existence and local stability of equilibria are determined. The boundedness of solutions, the existence of a limit cycle and a separatrix curve are also proven. Besides, the main properties of the model are examined from an ecological point of view. To make a comparative discussion of our results, an Appendix is added with the main properties of models, in which neither the Allee effect nor the competition among predators is considered. Some simulations are shown to endorse our results.

DEFINITION AND APPLICATIONS OF THE ASCENT-PROBABILITY DISTRIBUTION IN ONE-DIMENSIONAL MAPS

2009 ◽  
Vol 19 (11) ◽  
pp. 3567-3591 ◽  
Author(s):  
GEORGE LIVADIOTIS
Keyword(s):  
Invariant Measure ◽  
Rotation Number ◽  
Logistic Map ◽  
Discrete Distribution ◽  
Nonlinear Parameter ◽  
Invariant Density ◽  
One Dimensional ◽  
One Dimensional Maps ◽  
Parameter Values ◽  
Specific Number

This paper introduces the discrete distribution of ascent probabilities [Formula: see text], generalizing the concept of rotation number ω, already being defined in one-dimensional unimodal maps. The map domain is partitioned into subintervals [Formula: see text], each one containing orbits with their route characterized by a specific number of n successive ascents before a descent occurs. Then, Pn is defined as the probability to have an orbit performing n successive ascents, and equals the portion of the invariant measure within In. The rotation number is found to be equal to ω = P0 = P1, that is the portion of invariant measure within I0 or I1. Some significant applications of this relation concern (i) the rotation number dependence on the nonlinear parameter p, (ii) the analytical derivation of the rotation number, given the invariant density explicit expression, (iii) an easy computation of the rotation number that characterizes a periodic window. Moreover, the dependence of the ascent probabilities on the nonlinear parameter p is examined. Emphasis is placed on the discrete distribution of the ascent probabilities [Formula: see text] within the chaotic zone. A particular set of nonlinear parameter values [Formula: see text] is affiliated to the concept of ascent probabilities: For each probability Pn, n = 0, 1, 2, …, there is a lower limit of the nonlinear parameter values, p(n+1), so that, Pn = 0 ∀ p ≤ p(n+1). The set [Formula: see text] is analytically determined, and its specific arrangement in the chaotic zone is studied. Finally, the "u-S-P equivalence" between the triplet of the set of the fixed point and its preimages, [Formula: see text], of the invariant density S, and of the set of the ascents probabilities, [Formula: see text], is formulated. In particular, we show that each component of this triplet can be estimated whenever the other two components are given. Applications in the case of Logistic map are thoroughly examined.

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