Complex Dynamics of an Autonomous Prey-Predator System with Impulsive State Feedback Control

2009 ◽  
Author(s):  
Zuoliang Xiong ◽  
Xin Wang ◽  
Shunyi Li
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Complex Dynamics ◽  
State Feedback Control ◽  
Impulsive State Feedback Control ◽  
Predator System

scholarly journals Mathematical and Dynamic Analysis of a Prey-Predator Model in the Presence of Alternative Prey with Impulsive State Feedback Control

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Chuanjun Dai ◽  
Min Zhao
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Alternative Prey ◽  
Bifurcation Diagrams ◽  
Impulsive State Feedback Control ◽  
Existence And Stability ◽  
Predator Model ◽  
Predator System

The dynamic complexities of a prey-predator system in the presence of alternative prey with impulsive state feedback control are studied analytically and numerically. By using the analogue of the Poincaré criterion, sufficient conditions for the existence and stability of semitrivial periodic solutions can be obtained. Furthermore, the corresponding bifurcation diagrams and phase diagrams are investigated by means of numerical simulations which illustrate the feasibility of the main results.

scholarly journals Dynamic Complexity of an Ivlev-Type Prey-Predator System with Impulsive State Feedback Control

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Chuanjun Dai ◽  
Min Zhao ◽  
Lansun Chen
Keyword(s):  
Feedback Control ◽  
Numerical Simulations ◽  
State Feedback ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Bifurcation Diagrams ◽  
Dynamic Complexity ◽  
Impulsive State Feedback Control ◽  
The Stability ◽  
Predator System

The dynamic complexities of an Ivlev-type prey-predator system with impulsive state feedback control are studied analytically and numerically. Using the analogue of the Poincaré criterion, sufficient conditions for the existence and the stability of semitrivial periodic solutions can be obtained. Furthermore, the bifurcation diagrams and phase diagrams are investigated by means of numerical simulations, which illustrate the feasibility of the main results presented here.

scholarly journals Chemostat Model of Competition between Plasmid-Bearing and Plasmid-Free Organism with the Impulsive State Feedback Control

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Fengmei Tao ◽  
Zhong Zhao ◽  
Lansun Chen
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Impulsive Control ◽  
Continuous System ◽  
Threshold Value ◽  
State Feedback Control ◽  
Qualitative Properties ◽  
Chemostat Model ◽  
Impulsive State Feedback Control ◽  
The Stability

In this paper, we propose a chemostat model of competition between plasmid-bearing and plasmid-free organism with the impulsive state feedback control. The sufficient condition for existence of the positive period-1 solution is obtained by means of successor function and the qualitative properties of the corresponding continuous system. We show that the impulsive control system is more effective than the corresponding continuous system if we choose a suitable threshold value of the state feedback control in the process of manufacturing the desired products through genetically modified techniques. Furthermore, a new method of proving the stability of the order-1 periodic solution is given based on the theory of the limit cycle of the continuous dynamical system. Finally, mathematical results are justified by some numerical simulations.

Studies on the dynamics of a continuous bioprocess with impulsive state feedback control☆

2010 ◽  
Vol 157 (2-3) ◽  
pp. 558-567 ◽  
Author(s):  
Yuan Tian ◽  
Kaibiao Sun ◽  
Lansun Chen ◽  
Andrzej Kasperski
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
State Feedback Control ◽  
Impulsive State Feedback Control

scholarly journals A Pest Management Model with Stage Structure and Impulsive State Feedback Control

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Guoping Pang ◽  
Zhiqing Liang ◽  
Weijian Xu ◽  
Lijie Li ◽  
Gang Fu
Keyword(s):  
Periodic Solution ◽  
Feedback Control ◽  
Pest Management ◽  
State Feedback ◽  
Stage Structure ◽  
State Feedback Control ◽  
Management Model ◽  
Continuous Systems ◽  
Impulsive State Feedback Control ◽  
The Stability

A pest management model with stage structure and impulsive state feedback control is investigated. We get the sufficient condition for the existence of the order-1 periodic solution by differential equation geometry theory and successor function. Further, we obtain a new judgement method for the stability of the order-1 periodic solution of the semicontinuous systems by referencing the stability analysis for limit cycles of continuous systems, which is different from the previous method of analog of Poincarè criterion. Finally, we analyze numerically the theoretical results obtained.

Impulsive state feedback control during the sulphitation reaction in process of manufacture of sugar

2020 ◽  
pp. 2050076
Author(s):  
Guoping Pang ◽  
Xianbo Sun ◽  
Zhiqing Liang ◽  
Silian He ◽  
Xiaping Zeng
Keyword(s):  
Periodic Solution ◽  
Feedback Control ◽  
Limit Cycles ◽  
Switched Systems ◽  
State Feedback ◽  
State Feedback Control ◽  
Continuous Systems ◽  
Stability Criteria ◽  
Impulsive State Feedback Control ◽  
Existence And Stability

In this paper, the system with impulsive state feedback control corresponding to the sulphitation reaction in process of manufacture of sugar is considered. By means of square approximation and a series of switched systems, the periodic solution is approximated by a series of continuous hybrid limit cycles. Similar to the analysis of limit cycles of continuous systems, the existence and stability criteria of the order-1 periodic solution are obtained. Further, numerical analysis and discussion are given.

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