Control and Synchronization of Julia Sets in the Forced Brusselator Model

2015 ◽  
Vol 25 (09) ◽  
pp. 1550113 ◽  
Author(s):  
Weihua Sun ◽  
Yongping Zhang
Keyword(s):  
Feedback Control ◽  
Numerical Simulations ◽  
Julia Set ◽  
Julia Sets ◽  
The Other ◽  
Discrete Version ◽  
Brusselator Model ◽  
Control And Synchronization ◽  
And Control

The forced Brusselator model is investigated from the fractal viewpoint. A Julia set of the discrete version of the Brusselator model is introduced and control of the Julia set is presented by using feedback control. In order to discuss the relations of two different Julia sets, a coupled item is designed to realize the synchronization of two Julia sets with different parameters, which provides a method to discuss the relation and the changing of two different Julia sets, one Julia set can be changed to be the other. Numerical simulations are used to verify the effectiveness of these methods.

Fractal analysis and control of the competition model

2016 ◽  
Vol 09 (03) ◽  
pp. 1650045 ◽  
Author(s):  
Mianmian Zhang ◽  
Yongping Zhang
Keyword(s):  
Feedback Control ◽  
Mathematical Models ◽  
Fractal Analysis ◽  
Fractal Geometry ◽  
Julia Set ◽  
Julia Sets ◽  
Competition Model ◽  
Simulation Results ◽  
Population Competition ◽  
And Control

Lotka–Volterra population competition model plays an important role in mathematical models. In this paper, Julia set of the competition model is introduced by use of the ideas and methods of Julia set in fractal geometry. Then feedback control is taken on the Julia set of the model. And synchronization of two different Julia sets of the model with different parameters is discussed, which makes one Julia set change to be another. The simulation results show the efficacy of these methods.

scholarly journals Control and synchronization of Julia sets of the complex dissipative standard system

2016 ◽  
Vol 21 (4) ◽  
pp. 465-476
Author(s):  
Weihua Sun ◽  
Yongping Zhang
Keyword(s):  
Control Parameter ◽  
Julia Set ◽  
Julia Sets ◽  
The Other ◽  
Standard System ◽  
Control And Synchronization ◽  
Backward Orbits

The fractal behaviors of the complex dissipative standard system are discussed in this paper. By using the boundedness of the forward and backward orbits, Julia set of the system is introduced and visualization of Julia set is also given. Then a controller is designed to achieve Julia set shrinking or expanding with the changing of the control parameter. And synchronization of two different Julia sets is discussed by adding a coupling item, which makes one Julia set change to be the other. The simulations illustrate the efficacy of these methods.

scholarly journals Chaos and Control in Coronary Artery System

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Yanxiang Shi
Keyword(s):  
Coronary Artery ◽  
Feedback Control ◽  
Numerical Simulations ◽  
Melnikov Method ◽  
Phase Portraits ◽  
Bifurcation Diagrams ◽  
Nonlinear Dynamical ◽  
The Road ◽  
Two Systems ◽  
And Control

Two types of coronary artery system N-type and S-type, are investigated. The threshold conditions for the occurrence of Smale horseshoe chaos are obtained by using Melnikov method. Numerical simulations including phase portraits, potential diagram, homoclinic bifurcation curve diagrams, bifurcation diagrams, and Poincaré maps not only prove the correctness of theoretical analysis but also show the interesting bifurcation diagrams and the more new complex dynamical behaviors. Numerical simulations are used to investigate the nonlinear dynamical characteristics and complexity of the two systems, revealing bifurcation forms and the road leading to chaotic motion. Finally the chaotic states of the two systems are effectively controlled by two control methods: variable feedback control and coupled feedback control.

CONTROL AND SYNCHRONIZATION OF JULIA SETS OF THE COMPLEX PERTURBED RATIONAL MAPS

2013 ◽  
Vol 23 (05) ◽  
pp. 1350083 ◽  
Author(s):  
YONGPING ZHANG
Keyword(s):  
Optimal Control ◽  
Function Method ◽  
Control Method ◽  
Control Function ◽  
Julia Set ◽  
Julia Sets ◽  
Rational Maps ◽  
Control And Synchronization ◽  
Function Synchronization ◽  
Optimal Control Function

The dynamical and fractal behaviors of the complex perturbed rational maps [Formula: see text] are discussed in this paper. And the optimal control function method is taken on the Julia set of this system. In this control method, infinity is regarded as a fixed point to be controlled. By substituting the driving item for an item in the optimal control function, synchronization of Julia sets of two such different systems is also studied.

Extinction in a discrete Lotka–Volterra competitive system with the effect of toxic substances and feedback controls

2015 ◽  
Vol 08 (01) ◽  
pp. 1550012 ◽  
Author(s):  
Lijuan Chen ◽  
Fengde Chen
Keyword(s):  
Feedback Control ◽  
Lyapunov Function ◽  
Numerical Simulations ◽  
Sufficient Conditions ◽  
The Other ◽  
Toxic Substances ◽  
Two Dimensional ◽  
Competitive System ◽  
Feedback Controls ◽  
Analysis Technique

In this paper, we consider a discrete Lotka–Volterra competitive system with the effect of toxic substances and feedback controls. By using the method of discrete Lyapunov function and by developing a new analysis technique, we obtain the sufficient conditions which guarantee that one of the two species will be driven to extinction while the other will be permanent. We improve the corresponding results of Li and Chen [Extinction in two-dimensional discrete Lotka–Volterra competitive system with the effect of toxic substances, Dynam. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 15 (2008) 165–178]. Also, an example together with their numerical simulations shows the feasibility of our main results. It is shown that toxic substances and feedback control variables play an important role in the dynamics of the system.

Fractal dimension and synchronization of the controlled Julia sets of the SIRS model

2019 ◽  
Vol 12 (07) ◽  
pp. 1950085
Author(s):  
Miao Ouyang ◽  
Yongping Zhang ◽  
Jian Liu
Keyword(s):  
Infectious Disease ◽  
Fractal Dimension ◽  
System Simulation ◽  
Julia Set ◽  
Julia Sets ◽  
Discrete Version ◽  
Nonlinear Coupling ◽  
Box Counting ◽  
Sirs Model ◽  
Simulation Results

It is of crucial significance to study the infectious disease phenomenon by using the SIRS model and thoughts of Julia set. In this paper, Julia set of the discrete version of the SIRS model is established to analyze the fractal dynamics of this model. Then, controller is designed to change the Julia set. Furthermore, the box-counting dimensions of the controlled Julia sets by selecting different appropriate parameters are computed to show the complexity of the model. Finally, a nonlinear coupling method is introduced to synchronize the Julia sets with different parameters of the same system. Simulation results show the efficacy of these methods.

scholarly journals Consensus of Julia Sets

2022 ◽  
Vol 6 (1) ◽  
pp. 43
Author(s):  
Weihua Sun ◽  
Shutang Liu
Keyword(s):  
Fractal Theory ◽  
Julia Set ◽  
Julia Sets ◽  
The Other ◽  
Multi Agent Systems ◽  
Practical Applications ◽  
Agent Systems ◽  
Multi Agent

The Julia set is one of the most important sets in fractal theory. The previous studies on Julia sets mainly focused on the properties and graph of a single Julia set. In this paper, activated by the consensus of multi-agent systems, the consensus of Julia sets is introduced. Moreover, two types of the consensus of Julia sets are proposed: one is with a leader and the other is with no leaders. Then, controllers are designed to achieve the consensus of Julia sets. The consensus of Julia sets allows multiple different Julia sets to be coupled. In practical applications, the consensus of Julia sets provides a tool to study the consensus of group behaviors depicted by a Julia set. The simulations illustrate the efficacy of these methods.

Prothrombin Time Standardization: Report of the Expert Panel on Oral Anticoagulant Control

1979 ◽  
Vol 42 (04) ◽  
pp. 1073-1114 ◽  
Keyword(s):  
Prothrombin Time ◽  
Expert Panel ◽  
The Other ◽  
Rabbit Brain ◽  
Calibration Constant ◽  
Freeze Dried ◽  
The Mean ◽  
Point Of Intersection ◽  
And Control ◽  
Standardization Report

SummaryIn collaborative experiments in 199 laboratories, nine commercial thromboplastins, four thromboplastins held by the National Institute for Biological Standards and Control (NIBS & C), London and the British Comparative Thromboplastin were tested on fresh normal and coumarin plasmas, and on three series of freeze-dried plasmas. One of these was made from coumarin plasmas and the other two were prepared from normal plasmas; in each series, one plasma was normal and the other two represented different degrees of coumarin defect.Each thromboplastin was calibrated against NIBS&C rabbit brain 70/178, from the slope of the line joining the origin to the point of intersection of the mean ratios of coumarin/normal prothrombin times when the ratios obtained with the two thromboplastins on the same fresh plasmas were plotted against each other. From previous evidence, the slopes were calculated which would have been obtained against the NIBS&C “research standard” thromboplastin 67/40, and termed the “calibration constant” of each thromboplastin. Values obtained from the freeze-dried coumarin plasmas gave generally similar results to those from fresh plasmas for all thromboplastins, whereas values from the artificial plasmas agreed with those from fresh plasmas only when similar thromboplastins were being compared.Taking into account the slopes of the calibration lines and the variation between laboratories, precision in obtaining a patient’s prothrombin time was similar for all thromboplastins.

Dry chip feedrate control using online chip moisture

TAPPI Journal ◽  
2018 ◽  
Vol 17 (05) ◽  
pp. 295-305
Author(s):  
Wesley Gilbert ◽  
Ivan Trush ◽  
Bruce Allison ◽  
Randy Reimer ◽  
Howard Mason
Keyword(s):  
Production Rate ◽  
Control Strategy ◽  
Rate Control ◽  
Near Infrared ◽  
Dry Mass ◽  
The Other ◽  
Process Variability ◽  
Moisture Sensor ◽  
Feedback Control Strategy ◽  
And Control

Normal practice in continuous digester operation is to set the production rate through the chip meter speed. This speed is seldom, if ever, adjusted except to change production, and most of the other digester inputs are ratioed to it. The inherent assumption is that constant chip meter speed equates to constant dry mass flow of chips. This is seldom, if ever, true. As a result, the actual production rate, effective alkali (EA)-to-wood and liquor-to-wood ratios may vary substantially from assumed values. This increases process variability and decreases profits. In this report, a new continuous digester production rate control strategy is developed that addresses this shortcoming. A new noncontacting near infrared–based chip moisture sensor is combined with the existing weightometer signal to estimate the actual dry chip mass feedrate entering the digester. The estimated feedrate is then used to implement a novel feedback control strategy that adjusts the chip meter speed to maintain the dry chip feedrate at the target value. The report details the results of applying the new measurements and control strategy to a dual vessel continuous digester.

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