scholarly journals Feedback Control Variables Have No Influence on the Permanence of a Discreten-Species Schoener Competition System with Time Delays

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Qianqian Su ◽  
Na Zhang
Keyword(s):  
Feedback Control ◽  
Numerical Simulations ◽  
Time Delays ◽  
Feedback Controls ◽  
Control Variables ◽  
Difference Inequality ◽  
Competition System ◽  
Inequality Theory

We consider a discreten-species Schoener competition system with time delays and feedback controls. By using difference inequality theory, a set of conditions which guarantee the permanence of system is obtained. The results indicate that feedback control variables have no influence on the persistent property of the system. Numerical simulations show the feasibility of our results.

scholarly journals Permanence for a Discrete Ratio-Dependent Predator-Prey System with Holling Type III Functional Response and Feedback Controls

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Jiangbin Chen ◽  
Shengbin Yu
Keyword(s):  
Feedback Control ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Feedback Controls ◽  
Control Variables ◽  
Predator Prey ◽  
Type Iii ◽  
Prey System ◽  
Ratio Dependent

A new set of sufficient conditions for the permanence of a ratio-dependent predator-prey system with Holling type III functional response and feedback controls are obtained. The result shows that feedback control variables have no influence on the persistent property of the system, thus improving and supplementing the main result of Yang (2008).

scholarly journals Feedback Control Variables Have No Influence on the Permanence of a DiscreteN-Species Cooperation System

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
Author(s):  
Liujuan Chen ◽  
Xiangdong Xie ◽  
Lijuan Chen
Keyword(s):  
Feedback Control ◽  
Sufficient Conditions ◽  
Cooperative System ◽  
Feedback Controls ◽  
Control Variables ◽  
Cooperation System

A new set of sufficient conditions for the permanence of a discreteN-species cooperation system with delays and feedback controls are obtained. Our result shows that feedback control variables have no influence on the persistent property of the discrete cooperative system, thus improves and supplements the main result of F. D. Chen (2007).

scholarly journals Permanence in a Discrete Mutualism Model with Infinite Deviating Arguments and Feedback Controls

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Changjin Xu ◽  
Yusen Wu
Keyword(s):  
Sufficient Conditions ◽  
Feedback Controls ◽  
Difference Inequality ◽  
Deviating Arguments ◽  
Inequality Theory ◽  
The Difference ◽  
Mutualism Model

We propose and deal with a discrete mutualism model with infinite deviating arguments and feedback controls. Sufficient conditions which guarantee the permanence of the system are obtained by using the difference inequality theory. The paper ends with brief conclusions.

scholarly journals GLOBAL DYNAMICS OF A COMPUTER VIRUS PROPAGATION MODEL WITH FEEDBACK CONTROLS

2020 ◽  
Vol 36 (4) ◽  
pp. 295-304 ◽  
Author(s):  
Quang A Dang ◽  
Manh Tuan Hoang ◽  
Dinh Hung Tran
Keyword(s):  
Numerical Simulations ◽  
Computer Virus ◽  
Propagation Model ◽  
Global Dynamics ◽  
Virus Propagation ◽  
Feedback Controls ◽  
Control Variables ◽  
Differential Model ◽  
Mathematical Analyses ◽  
Computer Virus Propagation Model

A computer virus propagation model with feedback controls is first proposed and investigated. We show that the control variables do not influence on the global stability of the original differential model, they only alter the position of the unique viral equilibrium. The mathematical analyses and numerical simulations show that this equilibrium can be completely eliminated, namely, moved to the origin of coordinates if suitable values of the control variables are chosen. In the other words, the control variables are effective in the prevention of viruses in computer systems. Some numerical simulations are presented to demonstrate the validity of the obtained theoretical results.   

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.

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.

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