scholarly journals Dynamical Analysis of a Pest Management Model with Saturated Growth Rate and State Dependent Impulsive Effects

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Wencai Zhao ◽  
Tongqian Zhang ◽  
Xinzhu Meng ◽  
Yang Yang
Keyword(s):  
Differential Equation ◽  
Pest Management ◽  
Impulsive Differential Equation ◽  
Dynamical Analysis ◽  
Management Model ◽  
State Dependent ◽  
Existence And Stability ◽  
Focus Point ◽  
New Pest ◽  
Ipm Strategy

A new pest management mathematical model with saturated growth is proposed. The integrated pest management (IPM) strategy by introducing two state dependent pulses into the model is considered. Firstly, we analyze singular points of the model qualitatively and get the condition for focus point. Secondly, by using geometry theory of impulsive differential equation, the existence and stability of periodic solution of the system are discussed. Lastly, some examples and numerical simulations are given to illustrate our results.

scholarly journals Periodic Solutions Generated by Impulses for State-Dependent Impulsive Differential Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Qizhen Xiao ◽  
Binxiang Dai
Keyword(s):  
Differential Equation ◽  
Numerical Simulations ◽  
Periodic Solutions ◽  
Impulsive Differential Equation ◽  
Geometrical Analysis ◽  
Differential Systems ◽  
Impulsive Differential Systems ◽  
Analysis Methods ◽  
State Dependent ◽  
Existence Of Periodic Solutions

We study the existence of periodic solutions for a class of state-dependent impulsive differential systems via geometrical analysis methods. Our results show that these periodic solutions are generated by impulses. Moreover, numerical simulations are used to examine the existence of the periodic solutions.

scholarly journals Multi-State Dependent Impulsive Control for Pest Management

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Huidong Cheng ◽  
Fang Wang ◽  
Tongqian Zhang
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Qualitative Analysis ◽  
Pest Management ◽  
Pest Control ◽  
Impulsive Control ◽  
Management Strategies ◽  
Control Methods ◽  
State Dependent ◽  
Order One Periodic Solution

According to the integrated pest management strategies, we propose a model for pest control which adopts different control methods at different thresholds. By using differential equation geometry theory and the method of successor functions, we prove the existence of order one periodic solution of such system, and further, 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. Our results 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.

Dynamical analysis of a two-species competitive system with state feedback impulsive control

2020 ◽  
Vol 13 (05) ◽  
pp. 2050007
Author(s):  
Jing Xu ◽  
Mingzhan Huang ◽  
Xinyu Song
Keyword(s):  
Periodic Solution ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Dynamical Analysis ◽  
Competitive System ◽  
Competitive Systems ◽  
State Dependent ◽  
Existence And Stability ◽  
The Stability ◽  
Theoretical Results

In this paper, three competitive systems with different kinds of state-dependent control are presented and investigated. The existence of the order-1 homoclinic orbit and order-1 periodic solution of the two systems that incorporate just one kind of state-dependent control is obtained by applying differential equation geometry theory, and the stability of the order-1 periodic solution of each system is also given. Besides, sufficient conditions for the existence and stability of the order-2 periodic solution of the system that incorporate two kinds of state-dependent control are gained by successor function method and analogue of Poincaré criterion, respectively. Finally, numerical simulations are carried out to verify the theoretical results.

Dynamics on tumor immunotherapy model with periodic impulsive infusion

2016 ◽  
Vol 09 (05) ◽  
pp. 1650079
Author(s):  
Huiyan Zhu ◽  
Qian Ding ◽  
Fangjuan Wang ◽  
Huilan Wang
Keyword(s):  
Differential Equation ◽  
Immune Cells ◽  
Impulsive Differential Equation ◽  
Tumor Immunotherapy ◽  
Transient Behavior ◽  
Equation Model ◽  
Model Solution ◽  
Floquet Multiplier ◽  
Differential Equation Model ◽  
Existence And Stability

A periodic pulse differential equation model of tumor immunotherapy is established by considering the periodic and transient behavior of infusing immune cells. Using comparison theorem and Floquet multiplier theory of the impulsive differential equation, the boundedness of the model solution, the existence and stability of the free-tumor periodic solution are given. Furthermore, the persistence of the system is analyzed. Numerical simulations are carried to confirm the main theorems.

Sign in / Sign up

Export Citation Format

Share Document