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 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 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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