scholarly journals The state-dependent impulsive control for a general predator–prey model

2021 ◽  
pp. 1-19
Author(s):  
Xiaoxiao Zhu ◽  
Huilan Wang ◽  
Zigen Ouyang
Keyword(s):  
Impulsive Control ◽  
The State ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
State Dependent

DYNAMICS ON A HOLLING II PREDATOR–PREY MODEL WITH STATE-DEPENDENT IMPULSIVE CONTROL

2012 ◽  
Vol 05 (03) ◽  
pp. 1260006 ◽  
Author(s):  
BING LIU ◽  
YE TIAN ◽  
BAOLIN KANG
Keyword(s):  
Periodic Solution ◽  
Chemical Control ◽  
Impulsive Control ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
State Dependent ◽  
Continuous Dynamic System ◽  
Continuous Dynamic ◽  
Holling Ii Functional Response

According to biological and chemical control strategy for pest control, a Holling II functional response predator–prey system concerning state-dependent impulsive control is investigated. We define the successor functions of semi-continuous dynamic system and give an existence theorem of order 1 periodic solution of such a system. By means of sequence convergence rules and qualitative analysis, we successfully get the conditions of existence and attractiveness of order 1 periodic solution. Our results show that our method used in this paper is more efficient and easier than the existing methods to prove the existence and attractiveness of order 1 periodic solution.

Modeling and analysis of a predator–prey model with state-dependent delay

2018 ◽  
Vol 11 (02) ◽  
pp. 1850026 ◽  
Author(s):  
Yunfei Lv ◽  
Yongzhen Pei ◽  
Rong Yuan
Keyword(s):  
Immature Stage ◽  
Global Dynamics ◽  
Modeling And Analysis ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Predator Prey Model ◽  
Prey Model ◽  
State Dependent ◽  
State Dependent Delay ◽  
Threshold Amount

We propose and study a predator–prey model with state-dependent delay where the prey population is assumed to have an age structure. The state-dependent delay appears due to the mature condition that the prey must spend an amount of time in the immature stage sufficient to accumulate a threshold amount of food. We perform a qualitative analysis of the solutions, which includes studying positivity and boundedness, existence and local stability of equilibria. For the global dynamics of the system, we discuss an attracting region which is determined by solutions, and the region collapses to the interior equilibrium in the constant delay case.

scholarly journals Dynamics of a predator-prey model with state-dependent carrying capacity

2017 ◽  
Vol 22 (11) ◽  
pp. 1-15
Author(s):  
Hanwu Liu ◽  
◽  
Lin Wang ◽  
Fengqin Zhang ◽  
Qiuying Li ◽  
...  
Keyword(s):  
Carrying Capacity ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
State Dependent

scholarly journals Multi-State Dependent Impulsive Control for Holling I Predator-Prey Model

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Huidong Cheng ◽  
Fang Wang ◽  
Tongqian Zhang
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Chemical Control ◽  
Impulsive Control ◽  
Control Methods ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
State Dependent ◽  
Order One Periodic Solution

According to the different effects of biological and chemical control, we propose a model for Holling I functional response predator-prey system concerning pest control which adopts different control methods at different thresholds. By using differential equation geometry theory and the method of successor functions, we prove that the existence of order one periodic solution of such system and the attractiveness of the order one periodic solution by sequence convergence rules and qualitative analysis. Numerical simulations are carried out to illustrate the feasibility of our main results which show that our method used in this paper is more efficient and easier than the existing ones for proving the existence of order one periodic solution.

scholarly journals Generalized Predator-Prey Model with Nonlinear Impulsive Control Strategy

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Wenjie Qin ◽  
Guangyao Tang ◽  
Sanyi Tang
Keyword(s):  
Pest Control ◽  
Impulsive Control ◽  
Dynamical Behavior ◽  
Limited Resource ◽  
Control Measures ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Pest Outbreaks ◽  
Wide Range

A generalized predator-prey model concerning integrated pest management and nonlinear impulsive control measures is proposed and analyzed. The main purpose is to understand how resource limitation affects the successful pest control and pest outbreaks. The threshold conditions for the stability of the pest-free periodic solution are given firstly. Once the threshold value exceeds a critical level, both pest and its natural enemy populations can oscillate periodically. Secondly, in order to address how the limited resources affect the pest control, as an example the Holling II functional response function is chosen. The numerical results show that predator-prey model with limited resource has complex dynamical behavior. In addition, it is confirmed that the model has the coexistence of pests and natural enemies for a wide range of parameters.

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