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 Periodic Solution of Prey-Predator Model with Beddington-DeAngelis Functional Response and Impulsive State Feedback Control

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Chunjin Wei ◽  
Lansun Chen
Keyword(s):  
Periodic Solution ◽  
Feedback Control ◽  
Functional Response ◽  
State Feedback ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Impulsive Effects ◽  
Impulsive State Feedback Control ◽  
Predator Model ◽  
Order One Periodic Solution

A prey-predator model with Beddington-DeAngelis functional response and impulsive state feedback control is investigated. We obtain the sufficient conditions of the global asymptotical stability of the system without impulsive effects. By using the geometry theory of semicontinuous dynamic system and the method of successor function, we obtain the system with impulsive effects that has an order one periodic solution, and sufficient conditions for existence and stability of order one periodic solution are also obtained. Finally, numerical simulations are performed to illustrate our main results.

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.

Microbial insecticide model and homoclinic bifurcation of impulsive control system

2021 ◽  
pp. 2150043
Author(s):  
Tieying Wang
Keyword(s):  
Periodic Solution ◽  
Feedback Control ◽  
Homoclinic Orbit ◽  
State Feedback ◽  
Homoclinic Bifurcation ◽  
State Feedback Control ◽  
Global Dynamics ◽  
Impulsive State Feedback Control ◽  
Microbial Insecticide ◽  
Existence And Stability

A new microbial insecticide mathematical model with density dependent for pest is proposed in this paper. First, the system without impulsive state feedback control is considered. The existence and stability of equilibria are investigated and the properties of equilibria under different conditions are verified by using numerical simulation. Since the system without pulse has two positive equilibria under some additional assumptions, the system is not globally asymptotically stable. Based on the stability analysis of equilibria, limit cycle, outer boundary line and Sotomayor’s theorem, the existence of saddle-node bifurcation and global dynamics of the system are obtained. Second, we consider homoclinic bifurcation of the system with impulsive state feedback control. The existence of order-1 homoclinic orbit of the system is studied. When the impulsive function is slightly disturbed, the homoclinic orbit breaks and bifurcates order-1 periodic solution. The existence and stability of order-1 periodic solution are obtained by means of theory of semi-continuous dynamic system.

scholarly journals Impulsive State Feedback Control of the Rhizosphere Microbial Degradation in the Wetland Plant

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Zhong Zhao ◽  
Liuyong Pang ◽  
Zhanping Zhao ◽  
Chengguang Luo
Keyword(s):  
Periodic Solution ◽  
Feedback Control ◽  
Microbial Degradation ◽  
State Feedback ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Control Measures ◽  
Positive Order ◽  
Impulsive State Feedback Control

The rhizosphere microbe plays an important role in removing the pollutant generated from industrial and agricultural production. To investigate the dynamics of the microbial degradation, a nonlinear mathematical model of the rhizosphere microbial degradation is proposed based on impulsive state feedback control. The sufficient conditions for existence of the positive order-1 or order-2 periodic solution are obtained by using the geometrical theory of the semicontinuous dynamical system. We show the impulsive control system tends to an order-1 periodic solution or order-2 periodic solution if the control measures are achieved during the process of the microbial degradation. Furthermore, mathematical results are justified by some numerical simulations.

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.

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