scholarly journals Dynamics of a Stage Structured Pest Control Model in a Polluted Environment with Pulse Pollution Input

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Bing Liu ◽  
Ling Xu ◽  
Baolin Kang
Keyword(s):  
Pest Control ◽  
Natural Enemies ◽  
Natural Enemy ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Control Model ◽  
Polluted Environment ◽  
Impulsive Delay ◽  
Impulsive Delay Differential Equation ◽  
Delay Differential

By using pollution model and impulsive delay differential equation, we formulate a pest control model with stage structure for natural enemy in a polluted environment by introducing a constant periodic pollutant input and killing pest at different fixed moments and investigate the dynamics of such a system. We assume only that the natural enemies are affected by pollution, and we choose the method to kill the pest without harming natural enemies. Sufficient conditions for global attractivity of the natural enemy-extinction periodic solution and permanence of the system are obtained. Numerical simulations are presented to confirm our theoretical results.

scholarly journals Dynamics of a Stage Structure Pest Control Model with Impulsive Effects at Different Fixed Time

2009 ◽  
Vol 2009 ◽  
pp. 1-15 ◽  
Author(s):  
Bing Liu ◽  
Ying Duan ◽  
Yinghui Gao
Keyword(s):  
Time Delay ◽  
Pest Control ◽  
Natural Enemies ◽  
Stage Structure ◽  
Threshold Level ◽  
Fixed Time ◽  
Control Model ◽  
Pest Population ◽  
Maturation Time ◽  
Maturation Time Delay

Many existing pest control models, which control pests by releasing natural enemies, neglect the effect that natural enemies may get killed. From this point of view, we formulate a pest control model with stage structure for the pest with constant maturation time delay (through-stage time delay) and periodic releasing natural enemies and natural enemies killed at different fixed time and perform a systematic mathematical and ecological study. By using the comparison theorem and analysis method, we obtain the conditions for the global attractivity of the pest-eradication periodic solution and permanence of the system. We also present a pest management strategy in which the pest population is kept under the economic threshold level (ETL) when the pest population is uniformly permanent. We show that maturation time delay, impulsive releasing, and killing natural enemies can bring great effects on the dynamics of the system. Numerical simulations confirm our theoretical results.

scholarly journals Modelling and Analysis of a Pest-Control Pollution Model with Integrated Control Tactics

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Yiping Chen ◽  
Zhijun Liu ◽  
Wenjie Qin
Keyword(s):  
Periodic Solution ◽  
Pest Control ◽  
Natural Enemies ◽  
Integrated Control ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Critical Value ◽  
Globally Asymptotically Stable ◽  
Holling Ii Functional Response ◽  
Theoretical Results

A hybrid impulsive pest control model with stage structure for pest and Holling II functional response is proposed and investigated, in which the effects of impulsive pesticide input in the environment and in the organism are considered. Sufficient conditions for global attractiveness of the pest-extinction periodic solution and permanence of the system are obtained, which show that there exists a globally asymptotically stable pest-extinction periodic solution when the number of natural enemies released is more than some critical value, whereas the system can be permanent when the number of natural enemies released is less than another critical value. Furthermore, numerical simulations are carried out to illustrate our theoretical results and facilitate their interpretation.

scholarly journals Global attractivity of positive periodic solutions for an impulsive delay periodic “food limited” population model

2006 ◽  
Vol 2006 ◽  
pp. 1-10 ◽  
Author(s):  
Jian Song
Keyword(s):  
Global Attractivity ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Delay Equation ◽  
Periodic Functions ◽  
Globally Asymptotically Stable ◽  
Periodic Property ◽  
Impulsive Delay ◽  
Impulsive Delay Differential Equation ◽  
Delay Differential

We will consider the following nonlinear impulsive delay differential equationN′(t)=r(t)N(t)((K(t)−N(t−mw))/(K(t)+λ(t)N(t−mw))), a.e.t>0,t≠tk,N(tk+)=(1+bk)N(tk),K=1,2,…, wheremis a positive integer,r(t),K(t),λ(t)are positive periodic functions of periodicω. In the nondelay case(m=0), we show that the above equation has a unique positive periodic solutionN*(t)which is globally asymptotically stable. In the delay case, we present sufficient conditions for the global attractivity ofN*(t). Our results imply that under the appropriate periodic impulsive perturbations, the impulsive delay equation preserves the original periodic property of the nonimpulsive delay equation. In particular, our work extends and improves some known results.

scholarly journals Global attractivity of a class of delay differential equations with impulses

2003 ◽  
Vol 45 (2) ◽  
pp. 271-284 ◽  
Author(s):  
Yuji Liu ◽  
Binggen Zhang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Impulsive Delay ◽  
Impulsive Delay Differential Equation ◽  
Delay Differential

AbstractIn this paper, we study the global attractivity of the zero solution of a particular impulsive delay differential equation. Some sufficient conditions that guarantee every solution of the equation converges to zero are obtained.

scholarly journals The Effect of Impulsive Diffusion on Dynamics of a Stage-Structured Predator-Prey System

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Jianjun Jiao
Keyword(s):  
Discrete Dynamical System ◽  
Stage Structure ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Discrete Time Delay ◽  
Impulsive Diffusion ◽  
Impulsive Delay ◽  
Globally Attractive ◽  
Impulsive Delay Differential Equation ◽  
Delay Differential

We investigate a predator-prey model with impulsive diffusion on predator and stage structure on prey. The globally attractive condition of prey-extinction periodic solution of the system is obtained by the stroboscopic map of the discrete dynamical system. The permanent condition of the system is also obtained by the theory of impulsive delay differential equation. The results indicate that the discrete time delay has influence on the dynamical behaviors of the system. Finally, some numerical simulations are carried out to support the analytic results.

scholarly journals Intercropping Rosemary (Rosmarinus officinalis) with Sweet Pepper (Capsicum annum) Reduces Major Pest Population Densities without Impacting Natural Enemy Populations

Insects ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 74
Author(s):  
Xiao-wei Li ◽  
Xin-xin Lu ◽  
Zhi-jun Zhang ◽  
Jun Huang ◽  
Jin-ming Zhang ◽  
...  
Keyword(s):  
Integrated Pest Management ◽  
Pest Management ◽  
Pest Control ◽  
Natural Enemies ◽  
Natural Enemy ◽  
Sweet Pepper ◽  
Population Densities ◽  
Pest Population ◽  
Major Pest ◽  
Population Suppression

Intercropping of aromatic plants provides an environmentally benign route to reducing pest damage in agroecosystems. However, the effect of intercropping on natural enemies, another element which may be vital to the success of an integrated pest management approach, varies in different intercropping systems. Rosemary, Rosmarinus officinalis L. (Lamiaceae), has been reported to be repellent to many insect species. In this study, the impact of sweet pepper/rosemary intercropping on pest population suppression was evaluated under greenhouse conditions and the effect of rosemary intercropping on natural enemy population dynamics was investigated. The results showed that intercropping rosemary with sweet pepper significantly reduced the population densities of three major pest species on sweet pepper, Frankliniella intonsa, Myzus persicae, and Bemisia tabaci, but did not affect the population densities of their natural enemies, the predatory bug, Orius sauteri, or parasitoid, Encarsia formosa. Significant pest population suppression with no adverse effect on released natural enemy populations in the sweet pepper/rosemary intercropping system suggests this could be an approach for integrated pest management of greenhouse-cultivated sweet pepper. Our results highlight the potential of the integration of alternative pest control strategies to optimize sustainable pest control.

scholarly journals About Positivity of Green's Functions for Nonlocal Boundary Value Problems with Impulsive Delay Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Alexander Domoshnitsky ◽  
Irina Volinsky
Keyword(s):  
Differential Equation ◽  
Existence And Uniqueness ◽  
Green's Functions ◽  
Green’S Functions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Uniqueness Of Solutions ◽  
Impulsive Delay ◽  
Impulsive Delay Differential Equation ◽  
Delay Differential

The impulsive delay differential equation is considered(Lx)(t)=x′(t)+∑i=1mpi(t)x(t-τi(t))=f(t), t∈[a,b],  x(tj)=βjx(tj-0), j=1,…,k, a=t0<t1<t2<⋯<tk<tk+1=b, x(ζ)=0, ζ∉[a,b],with nonlocal boundary conditionlx=∫abφsx′sds+θxa=c,  φ∈L∞a,b;  θ, c∈R.Various results on existence and uniqueness of solutions and on positivity/negativity of the Green's functions for this equation are obtained.

scholarly journals Exponential Stability of Impulsive Delay Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
G. L. Zhang ◽  
M. H. Song ◽  
M. Z. Liu
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Euler Method ◽  
Exponentially Stable ◽  
Impulsive Delay Differential Equations ◽  
Numerical Process ◽  
Impulsive Delay ◽  
Delay Differential

The main objective of this paper is to further investigate the exponential stability of a class of impulsive delay differential equations. Several new criteria for the exponential stability are analytically established based on Razumikhin techniques. Some sufficient conditions, under which a class of linear impulsive delay differential equations are exponentially stable, are also given. An Euler method is applied to this kind of equations and it is shown that the exponential stability is preserved by the numerical process.

scholarly journals A STAGE-STRUCTURED PREDATOR-PREY SI MODEL WITH DISEASE IN THE PREY AND IMPULSIVE EFFECTS

2013 ◽  
Vol 18 (4) ◽  
pp. 505-528 ◽  
Author(s):  
Tongqian Zhang ◽  
Xinzhu Meng ◽  
Yi Song ◽  
Tonghua Zhang
Keyword(s):  
Pest Management ◽  
Analytical Techniques ◽  
Stage Structure ◽  
Threshold Level ◽  
Pest Population ◽  
Predator Prey ◽  
Impulsive Delay Differential Equations ◽  
Si Model ◽  
Impulsive Delay ◽  
Delay Differential

This paper aims to develop a high-dimensional SI model with stage structure for both the prey (pest) and the predator, and then to investigate the dynamics of it. The model can be used for the study of Integrated Pest Management (IPM) which is a combination of constant pulse releasing of animal enemies and diseased pests at two different fixed moments. Firstly, we use analytical techniques for impulsive delay differential equations to obtain the conditions for global attractivity of the ‘pest-free’ periodic solution and permanence of the population model. It shows that the conditions strongly depend on time delay, impulsive release of animal enemies and infective pests. Secondly, we present a pest management strategy in which the pest population is kept under the economic threshold level (ETL) when the pest population is permanent. Finally, numerical analysis is presented to illustrate our main conclusion.

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