scholarly journals Impulsive State Feedback Control of Cheese Whey Fermentation for Single-Cell Protein Production

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Chunjin Wei ◽  
Shuwen Zhang ◽  
Lansun Chen
Keyword(s):  
Periodic Solution ◽  
Feedback Control ◽  
State Feedback ◽  
Protein Production ◽  
Cheese Whey ◽  
Single Cell Protein ◽  
State Feedback Control ◽  
Cell Protein ◽  
Impulsive State Feedback Control ◽  
Single Cell Protein Production

The work is the analysis of a mathematical model of cheese whey fermentation for single-cell protein production with impulsive state feedback control. Through the analysis, the sufficient conditions of existence and stability of positive order-1 periodic solution are obtained. It is shown that the system either tends to a stable state or has a periodic solution, which depends on the feedback state, the control parameter of the dilution rate, and the initial concentrate of microorganism and substrate. For some special cases, it is also shown that the system may exist in order-2 periodic solution. Furthermore, our findings are confirmed by means of 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.

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.

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