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.

Bifurcations and chaos control in a discrete-time biological model

2020 ◽  
Vol 13 (04) ◽  
pp. 2050022 ◽  
Author(s):  
A. Q. Khan ◽  
T. Khalique
Keyword(s):  
Discrete Time ◽  
Chaos Control ◽  
Control Method ◽  
Complex Dynamics ◽  
Small Neighborhood ◽  
Positive Equilibrium ◽  
Global Dynamics ◽  
Flip Bifurcation ◽  
Time Model ◽  
Predator Prey Model

In this paper, bifurcations and chaos control in a discrete-time Lotka–Volterra predator–prey model have been studied in quadrant-[Formula: see text]. It is shown that for all parametric values, model has boundary equilibria: [Formula: see text], and the unique positive equilibrium point: [Formula: see text] if [Formula: see text]. By Linearization method, we explored the local dynamics along with different topological classifications about equilibria. We also explored the boundedness of positive solution, global dynamics, and existence of prime-period and periodic points of the model. It is explored that flip bifurcation occurs about boundary equilibria: [Formula: see text], and also there exists a flip bifurcation when parameters of the discrete-time model vary in a small neighborhood of [Formula: see text]. Further, it is also explored that about [Formula: see text] the model undergoes a N–S bifurcation, and meanwhile a stable close invariant curves appears. From the perspective of biology, these curves imply that between predator and prey populations, there exist periodic or quasi-periodic oscillations. Some simulations are presented to illustrate not only main results but also reveals the complex dynamics such as the orbits of period-2,3,13,15,17 and 23. The Maximum Lyapunov exponents as well as fractal dimension are computed numerically to justify the chaotic behaviors in the model. Finally, feedback control method is applied to stabilize chaos existing in the model.

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.

BIFURCATION ANALYSIS AND CONTROL OF A PLANKTON–FISH MODEL WITH A DISTRIBUTION DELAY

2011 ◽  
Vol 11 (04) ◽  
pp. 857-879 ◽  
Author(s):  
XUE ZHANG ◽  
QINGLING ZHANG
Keyword(s):  
Center Manifold ◽  
Control Method ◽  
Distributed Delay ◽  
State Feedback Control ◽  
Positive Equilibrium ◽  
Center Manifold Theorem ◽  
Fish Model ◽  
Feedback Control Method ◽  
Positive Equilibrium Point ◽  
And Control

This paper studies a plankton–fish model with distributed delay in the context of marine plankton interaction together with predation by planktotrophic fish. The delay indicates that the growth of the zooplankton depends on the past density of phytoplankton. The positive equilibrium point and its local stability are investigated. Using the average time delay as bifurcation parameter, we obtain the conditions of the existence of Hopf bifurcation. Based on the normal form and center manifold theorem, stability, direction, and other properties of bifurcating periodic solutions are derived. Moreover, a state feedback control method, which can be implemented by adjusting the harvesting for zooplankton population, is proposed to drive the plankton–fish system to a steady state. Numerical simulations illustrate the effectiveness of results and the related biological implications are discussed.

A Method of Finding Discrete Controls for Switched Dynamical Systems by Applying Continued Fractions

2021 ◽  
Vol 24 (2) ◽  
pp. 175-183
Author(s):  
S. M. Khryashchev
Keyword(s):  
Control Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Continued Fractions ◽  
Control Method ◽  
Initial State ◽  
Final State ◽  
Control Goal ◽  
Controllability Of Systems ◽  
And Control

Control systems with a finite number of control settings are considered. It is assumed that any polysystem operates in continuous time and control switchings occur at some certain discrete time instants. A control goal is to transfer a polysystem from an initial state to a final state. Controllability of systems switched in discrete time is studied. Controls are constructed by using the theory of generalized multicomponent continued fractions and the congruences theory. Applications of the proposed control method to specific systems are discussed.

System Identification and Control using Probabilistic Incremental Program Evolution Algorithm

2000 ◽  
Vol 12 (6) ◽  
pp. 675-681 ◽  
Author(s):  
Yuehui Chen ◽  
◽  
Shigeyasu Kawaji
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Prior Knowledge ◽  
Discrete Time ◽  
Control Method ◽  
Fitness Function ◽  
Operating Conditions ◽  
Learning Ability ◽  
Program Evolution ◽  
And Control

An indispensable ability for intelligent control is to comprehend and learn about plants, disturbances, environment, and operating conditions. In this paper, the Probabilistic Incremental Program Evolution (PIPE) algorithm, with its self-organizing and learning ability, is used as a promising tool for such purposes. The previous work on evolutionary control by using tree structure based evolutionary algorithm was inverse control in general. In this case, Genetic Programming (GP) was usually used to evolving a directly control law of nonlinear systems. It is difficult to design a better fitness function that should reflect the characteristics of nonlinear systems, and a prior knowledge about operating conditions is usually needed. In this paper, a new identification and control method is proposed without prior knowledge of the plant. Firstly, the input-output behavior of the discrete-time nonlinear system is approximated by the individual structure of PIPE (PIPE Emulator). Secondly, a model based evolutionary controller (PIPE Emulator-based controller) of nonlinear system is designed. Simulation results for a typical nonlinear discrete-time system show the feasibility and effectiveness of the proposed method.

scholarly journals Chaos and Control of Game Model Based on Heterogeneous Expectations in Electric Power Triopoly

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Weizhuo Ji
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Electric Power ◽  
Chaos Control ◽  
Control Method ◽  
Repeated Game ◽  
Game Model ◽  
Heterogeneous Expectations ◽  
Straight Line ◽  
And Control

A dynamic repeated game model has been established based on heterogeneous expectations in electric power triopoly. Theoretical analysis and numerical simulation show the complexity of this model; suppose that the producers make decisions with naive expectation and bounded rationality. The straight-line stabilization chaos control method was successfully applied to the dynamic repeated game model. The results have important practical value for the producers in the electric power oligopoly.

scholarly journals A new approach on the modelling, chaos control and synchronization of a fractional biological oscillator

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ali Saleh Alshomrani ◽  
Malik Zaka Ullah ◽  
Dumitru Baleanu
Keyword(s):  
Chaos Control ◽  
Control Method ◽  
Phase Portraits ◽  
New Approach ◽  
Control Scheme ◽  
Biological Oscillator ◽  
The Stability ◽  
Control And Synchronization ◽  
And Control ◽  
Active Control Method

AbstractThis research aims to discuss and control the chaotic behaviour of an autonomous fractional biological oscillator. Indeed, the concept of fractional calculus is used to include memory in the modelling formulation. In addition, we take into account a new auxiliary parameter in order to keep away from dimensional mismatching. Further, we explore the chaotic attractors of the considered model through its corresponding phase-portraits. Additionally, the stability and equilibrium point of the system are studied and investigated. Next, we design a feedback control scheme for the purpose of chaos control and stabilization. Afterwards, we introduce an efficient active control method to achieve synchronization between two chaotic fractional biological oscillators. The efficiency of the proposed stabilizing and synchronizing controllers is verified via theoretical analysis as well as simulations and numerical experiments.

AN ANALYSIS ON INSTANTANEOUS STABILITY OF AN ASSOCIATIVE CHAOTIC NEURAL NETWORK

1999 ◽  
Vol 09 (11) ◽  
pp. 2157-2163 ◽  
Author(s):  
MASAHARU ADACHI ◽  
KAZUYUKI AIHARA
Keyword(s):  
Neural Network ◽  
Discrete Time ◽  
Memory Retrieval ◽  
Chaotic Dynamics ◽  
Chaos Control ◽  
Dynamical Property ◽  
Neuron Models ◽  
Chaotic Neural Network ◽  
Time Step ◽  
Parameter Values

We analyze instantaneous stability of a chaotic neural network which shows nonperiodic associative dynamics. The network is composed of discrete-time neuron models of which individuals show chaotic dynamics with certain parameter values. The synaptic weights of the network are determined by an auto-associative matrix so that four binary patterns are stored as a basal memory of the network. It has been reported that the network retrieves stored patterns nonperiodically. However, the dynamical property of the network in each discrete-time step has not been clarified. In this paper, instantaneous stability of the network during the nonperiodic memory retrieval is analyzed by calculating eigenvalues of the Jacobian matrix. From the analysis, it is found that in every instance when the network retrieves stored patterns, all the eigenvalues are always less than unity. This implies that such states of the memory retrieval cannot be a target of the OGY-like chaos control methods.

Perencanaan Pengendalian Kualitas Produk Pakaian Bayi dengan Metode Six Sigma Pada CV. AGP

JEMAP ◽  
2020 ◽  
Vol 3 (1) ◽  
Author(s):  
Albertus Reynaldo Kurniawan ◽  
Bayu Prestianto
Keyword(s):  
Quality Control ◽  
Continuous Improvement ◽  
Six Sigma ◽  
Screen Printing ◽  
Control Method ◽  
Operational Performance ◽  
Machine Maintenance ◽  
Quality Product ◽  
Break Time ◽  
And Control

Quality control becomes an important key for companies in suppressing the number of defective produced products. Six Sigma is a quality control method that aims to minimize defective products to the lowest point or achieve operational performance with a sigma value of 6 with only yielding 3.4 defective products of 1 million product. Stages of Six Sigma method starts from the DMAIC (Define, Measure, Analyze, Improve and Control) stages that help the company in improving quality and continuous improvement. Based on the results of research on baby clothes products, data in March 2018 the percentage of defective products produced reached 1.4% exceeding 1% tolerance limit, with a Sigma value of 4.14 meaning a possible defect product of 4033.39 opportunities per million products. In the pareto diagram there were 5 types of CTQ (Critical to Quality) such as oblique obras, blobor screen printing, there is a fabric / head cloth code on the final product, hollow fabric / thin fabric fiber, and dirty cloth. The factors caused quality problems such as Manpower, Materials, Environtment, and Machine. Suggestion for consideration of company improvement was continuous improvement on every existing quality problem like in Manpower factor namely improving comprehension, awareness of employees in producing quality product and improve employee's accuracy, Strength Quality Control and give break time. Materials by making the method of cutting the fabric head, the Machine by scheduling machine maintenance and the provision of needle containers at each employees desk sewing and better environtment by installing exhaust fan and renovating the production room.

Sign in / Sign up

Export Citation Format

Share Document