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.

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 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 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.

scholarly journals Robust set stabilization of Boolean control networks with impulsive effects

2018 ◽  
Vol 23 (4) ◽  
pp. 553-567 ◽  
Author(s):  
Xiaojing Xu ◽  
Yansheng Liu ◽  
Haitao Li ◽  
Fuad E. Alsaadi
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
State Feedback Control ◽  
Impulsive Effects ◽  
Algebraic Form ◽  
Control Networks ◽  
Set Stabilization ◽  
Necessary And Sufficient

This paper addresses the robust set stabilization problem of Boolean control networks (BCNs) with impulsive effects via the semi-tensor product method. Firstly, the closed-loop system consisting of a BCN with impulsive effects and a given state feedback control is converted into an algebraic form. Secondly, based on the algebraic form, some necessary and sufficient conditions are presented for the robust set stabilization of BCNs with impulsive effects under a given state feedback control and a free-form control sequence, respectively. Thirdly, as applications, some necessary and sufficient conditions are presented for robust partial stabilization and robust output tracking of BCNs with impulsive effects, respectively. The study of two illustrative examples shows that the obtained new results are effective.

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