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 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 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.

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.

scholarly journals Dynamic Analysis of a Pest Management Smith Model with Impulsive State Feedback Control and Continuous Delay

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 591 ◽  
Author(s):  
Zhenzhen Shi ◽  
Yaning Li ◽  
Huidong Cheng
Keyword(s):  
Feedback Control ◽  
Periodic Orbit ◽  
Pest Management ◽  
State Feedback ◽  
State Feedback Control ◽  
Impulsive State Feedback Control ◽  
Continuous Delay ◽  
The Stability ◽  
Theoretical Results ◽  
Smith Model

In our paper, we propose a single population Smith model with continuous delay and impulsive state feedback control. The application in pest management of this model is investigated. First, the singularity of this model is qualitatively analyzed; then, we consider the existence and uniqueness of order-one periodic orbit in order to determine the frequency of the implementation of chemical control. Moreover, based on the limit method of the sequences of subsequent points, we verify the stability of periodic orbit to ensure a certain robustness of this control; at last, we carry out the numerical simulations to verify the correctness of the theoretical results.

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 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.

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
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