scholarly journals Stability and Permanence of a Pest Management Model with Impulsive Releasing and Harvesting

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Jiangtao Yang ◽  
Zhichun Yang
Keyword(s):  
Pest Management ◽  
Small Amplitude ◽  
Floquet Theory ◽  
Sufficient Conditions ◽  
Management Model ◽  
Perturbation Techniques ◽  
Globally Asymptotical Stability ◽  
Period Solution ◽  
Impulsive Releasing ◽  
Theoretical Results

We formulate a pest management model with periodically releasing infective pests, immature and mature natural enemies, and harvesting pests and crops at two different fixed moments. Sufficient conditions ensuring the locally and globally asymptotical stability of the susceptible pest-eradication period solution are found by means of Floquet theory, small amplitude perturbation techniques, and multicomparison results. Furthermore, the permanence of system is also derived. By numerical analysis, we also show that impulsive releasing and harvesting at two different fixed moments can bring obvious effects on the dynamics of system, which also corroborates our theoretical results.

The Pest Management Model with Impulsive Control

2014 ◽  
Vol 519-520 ◽  
pp. 1299-1304 ◽  
Author(s):  
Yan Song ◽  
Xuejuan Wang ◽  
Wei Jiang
Keyword(s):  
Pest Management ◽  
Control Strategy ◽  
Impulsive Control ◽  
Integrated Control ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Management Model ◽  
Globally Asymptotical Stability ◽  
Pest Eradication ◽  
Floquet Theorem

Based on integrated control strategy with spraying pesticides and releasing natural enemies at different fixed moments, we establish a pest management model with impulsive control. Using Floquet theorem of impulsive differential equations and comparison theorem, we obtain the sufficient conditions of globally asymptotical stability of the pest-eradication periodic solution and permanence of the model.

scholarly journals Extinction and Permanence of a Three-Species Lotka-Volterra System with Impulsive Control Strategies

2008 ◽  
Vol 2008 ◽  
pp. 1-18 ◽  
Author(s):  
Hunki Baek
Keyword(s):  
Chemical Control ◽  
Small Amplitude ◽  
Floquet Theory ◽  
Impulsive Control ◽  
Chaotic Behavior ◽  
Control Strategies ◽  
Perturbation Techniques ◽  
Top Predator ◽  
Volterra System ◽  
Comparison Results

A three-species Lotka-Volterra system with impulsive control strategies containing the biological control (the constant impulse) and the chemical control (the proportional impulse) with the same period, but not simultaneously, is investigated. By applying the Floquet theory of impulsive differential equation and small amplitude perturbation techniques to the system, we find conditions for local and global stabilities of a lower-level prey and top-predator free periodic solution of the system. In addition, it is shown that the system is permanent under some conditions by using comparison results of impulsive differential inequalities. We also give a numerical example that seems to indicate the existence of chaotic behavior.

THE PERIODIC VOLTERRA MODEL WITH MUTUAL INTERFERENCE AND IMPULSIVE EFFECT

2012 ◽  
Vol 05 (03) ◽  
pp. 1260005 ◽  
Author(s):  
YUJUAN ZHANG ◽  
LANSUN CHEN
Keyword(s):  
Periodic Solution ◽  
Bifurcation Theory ◽  
Floquet Theory ◽  
Sufficient Conditions ◽  
Mutual Interference ◽  
Volterra Model ◽  
Impulsive Effect ◽  
Special Cases ◽  
Coexistence State ◽  
Theoretical Results

In this paper, a periodic Volterra model with mutual interference and impulsive effect is proposed and analyzed. By applying the Floquet theory of impulsive differential equation, some conditions are obtained for the linear stability of semi-trivial periodic solution. Some sufficient conditions are also given for the permanence of the system. Further, standard bifurcation theory is used to show the existence of coexistence state which arises near the semi-trivial periodic solution. Finally, theoretical results are confirmed by some special cases of the system.

scholarly journals Dynamic Analysis of an Impulsive Predator-Prey Model with Disease in Prey and Ivlev-Type Functional Response

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Yuanfu Shao ◽  
Peiluan Li ◽  
Guoqiang Tang
Keyword(s):  
Functional Response ◽  
Small Amplitude ◽  
Floquet Theory ◽  
Complex Dynamics ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Pest Eradication ◽  
Disease In Prey

A predator-prey model with disease in prey, Ivlev-type functional response, and impulsive effects is proposed. By using Floquet theory and small amplitude perturbation skill, sufficient conditions of the existence and global stability of susceptible pest-eradication periodic solution are obtained. By impulsive comparison theorem, conditions ensuring the permanence of the system are established. Examples and simulation are given to show the complex dynamics for the key parameters.

Conditions for the local and global asymptotic stability of the time–fractional Degn–Harrison system

2020 ◽  
Vol 21 (7-8) ◽  
pp. 749-759
Author(s):  
Rachida Mezhoud ◽  
Khaled Saoudi ◽  
Abderrahmane Zaraï ◽  
Salem Abdelmalek
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Linearization Method ◽  
Direct Lyapunov Method ◽  
Fractional Systems ◽  
Reaction Diffusion Model ◽  
Theoretical Results

AbstractFractional calculus has been shown to improve the dynamics of differential system models and provide a better understanding of their dynamics. This paper considers the time–fractional version of the Degn–Harrison reaction–diffusion model. Sufficient conditions are established for the local and global asymptotic stability of the model by means of invariant rectangles, the fundamental stability theory of fractional systems, the linearization method, and the direct Lyapunov method. Numerical simulation results are used to illustrate the theoretical results.

Design Chaotic Neural Network from Discrete Time Feedback Function

2013 ◽  
Vol 339 ◽  
pp. 366-371
Author(s):  
Jin Sheng Ren ◽  
Guang Chun Luo ◽  
Ke Qin
Keyword(s):  
Discrete Time ◽  
Design Methodology ◽  
Universal Design ◽  
Jacobian Matrix ◽  
Sufficient Conditions ◽  
Neural Net ◽  
Chaotic Neural Network ◽  
Data Set ◽  
Dominant Matrix ◽  
Theoretical Results

The goal of this paper is to give a universal design methodology of a Chaotic Neural Net-work (CNN). By appropriately choosing self-feedback, coupling functions and external stimulus, we have succeeded in proving a dynamical system defined by discrete time feedback equations possess-ing interesting chaotic properties. The sufficient conditions of chaos are analyzed by using Jacobian matrix, diagonal dominant matrix and Lyapunov Exponent (LE). Experiments are also conducted un-der a simple data set. The results confirm the theorem's correctness. As far as we know, both the experimental and theoretical results presented here are novel.

scholarly journals Stability and Bogdanov-Takens Bifurcation of an SIS Epidemic Model with Saturated Treatment Function

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Yanju Xiao ◽  
Weipeng Zhang ◽  
Guifeng Deng ◽  
Zhehua Liu
Keyword(s):  
Sufficient Conditions ◽  
Global Dynamics ◽  
Sis Model ◽  
Delayed Treatment ◽  
Sis Epidemic Model ◽  
Treatment Function ◽  
Lyapunov Coefficient ◽  
Saturated Treatment ◽  
Theoretical Results ◽  
Disease Free

This paper introduces the global dynamics of an SIS model with bilinear incidence rate and saturated treatment function. The treatment function is a continuous and differential function which shows the effect of delayed treatment when the rate of treatment is lower and the number of infected individuals is getting larger. Sufficient conditions for the existence and global asymptotic stability of the disease-free and endemic equilibria are given in this paper. The first Lyapunov coefficient is computed to determine various types of Hopf bifurcation, such as subcritical or supercritical. By some complex algebra, the Bogdanov-Takens normal form and the three types of bifurcation curves are derived. Finally, mathematical analysis and numerical simulations are given to support our theoretical results.

scholarly journals Exponential Stability of Stochastic Differential Equation with Mixed Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Wenli Zhu ◽  
Jiexiang Huang ◽  
Xinfeng Ruan ◽  
Zhao Zhao
Keyword(s):  
Differential Equation ◽  
Time Delay ◽  
Stochastic Differential Equation ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Martingale Inequality ◽  
Mixed Delay ◽  
Exponentially Stable ◽  
Theoretical Results

This paper focuses on a class of stochastic differential equations with mixed delay based on Lyapunov stability theory, Itô formula, stochastic analysis, and inequality technique. A sufficient condition for existence and uniqueness of the adapted solution to such systems is established by employing fixed point theorem. Some sufficient conditions of exponential stability and corollaries for such systems are obtained by using Lyapunov function. By utilizing Doob’s martingale inequality and Borel-Cantelli lemma, it is shown that the exponentially stable in the mean square of such systems implies the almost surely exponentially stable. In particular, our theoretical results show that if stochastic differential equation is exponentially stable and the time delay is sufficiently small, then the corresponding stochastic differential equation with mixed delay will remain exponentially stable. Moreover, time delay upper limit is solved by using our theoretical results when the system is exponentially stable, and they are more easily verified and applied in practice.

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