scholarly journals A Mathematical Model for the Dynamics of a Fish Algae Consumption Model with Impulsive Control Strategy

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Jin Yang ◽  
Min Zhao
Keyword(s):  
Mathematical Model ◽  
Control Strategy ◽  
Floquet Theory ◽  
Impulsive Control ◽  
Impulsive Differential Equations ◽  
Asymptotically Stable ◽  
Perturbation Techniques ◽  
Globally Asymptotically Stable ◽  
The Rich ◽  
Impulsive Control Strategy

A dynamic mathematical model of fish algae consumption with an impulsive control strategy is proposed and analyzed in detail. It is shown that the system has a globally asymptotically stable algae-eradication periodic solution which can be obtained using the Floquet theory of impulsive differential equations and small-amplitude perturbation techniques. The conditions for the permanence of the system can also be determined. Numerical results for impulsive perturbations show the rich dynamic behavior of the system. All these results may be useful in controlling eutrophication.

scholarly journals Complex Behavior in a Fish Algae Consumption Model with Impulsive Control Strategy

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Jin Yang ◽  
Min Zhao
Keyword(s):  
Control Strategy ◽  
Small Amplitude ◽  
Impulsive Control ◽  
Asymptotically Stable ◽  
Perturbation Techniques ◽  
Globally Asymptotically Stable ◽  
Impulsive Equations ◽  
Consumption Model ◽  
The Rich ◽  
Impulsive Control Strategy

This paper investigates a dynamic mathematical model of fish algae consumption with an impulsive control strategy analytically. It is proved that the system has a globally asymptotically stable algae-eradication periodic solution and is permanent by using the theory of impulsive equations and small-amplitude perturbation techniques. Numerical results for impulsive perturbations demonstrate the rich dynamic behavior of the system. Further, we have also compared biological control with chemical control. All these results may be useful in controlling eutrophication.

DYNAMIC COMPLEXITIES IN A LOTKA–VOLTERRA PREDATOR–PREY MODEL CONCERNING IMPULSIVE CONTROL STRATEGY

2005 ◽  
Vol 15 (02) ◽  
pp. 517-531 ◽  
Author(s):  
BING LIU ◽  
YUJUAN ZHANG ◽  
LANSUN CHEN
Keyword(s):  
Periodic Solution ◽  
Control Strategy ◽  
Impulsive Control ◽  
Period Doubling ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Pest Eradication ◽  
Impulsive Control Strategy

Based on the classical Lotka–Volterra predator–prey system, an impulsive differential equation to model the process of periodically releasing natural enemies and spraying pesticides at different fixed times for pest control is proposed and investigated. It is proved that there exists a globally asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value. Otherwise, the system can be permanent. We observe that our impulsive control strategy is more effective than the classical one if we take chemical control efficiently. Numerical results show that the system we considered has more complex dynamics including period-doubling bifurcation, symmetry-breaking bifurcation, period-halving bifurcation, quasi-periodic oscillation, chaos and nonunique dynamics, meaning that several attractors coexist. Finally, a pest–predator stage-structured model for the pest concerning this kind of impulsive control strategy is proposed, and we also show that there exists a globally asymptotically stable pest-eradication periodic solution when the impulsive period is less than some threshold.

scholarly journals A Mathematical Model of Rabies Transmission Dynamics in Dogs Incorporating Public Health Education as a Control Strategy -A Case Study of Makueni County

2020 ◽  
pp. 1-11
Author(s):  
Jane S. Musaili ◽  
Isaac Chepkwony
Keyword(s):  
Public Health ◽  
Mathematical Model ◽  
Stability Analysis ◽  
Health Education ◽  
Control Strategy ◽  
Public Health Education ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Disease Free

Rabies is a zoonotic viral disease that aects all mammals including human beings. Dogs are responsible for 99% of human rabies cases and the disease is always fatal once the symptoms appear. In Kenya the disease is still endemic despite the fact that there are ecient vaccines for controlling the disease. In this project, we developed SIRS mathematical model using a system of ordinary dierential equations from the model to study the transmission dynamics of rabies virusin dogs using public health education as a control strategy. The reproduction number R0 was calculated using the Next Generation Matrix. Both disease free and endemics equilibrium points were determined and their stability analysis performed. From the stability analysis results it was found out that the disease free equilibrium point is both locally and globally asymptotically stable when R0 < 1 and the endemic equilibrium point is both locally and globally asymptotically stable when R0 > 1. Numerical simulations done using Matlab indicated that education of the public on administration of both pre and post exposure vaccines to dogs and responsible dog ownership leads to a decrease in the numbers of rabies virus infected dogs which shows that public health education is an ecient means for controlling rabies.

COMPLEX DYNAMICS OF ONE-PREY MULTI-PREDATOR SYSTEM WITH DEFENSIVE ABILITY OF PREY AND IMPULSIVE BIOLOGICAL CONTROL ON PREDATORS

2005 ◽  
Vol 08 (04) ◽  
pp. 483-495 ◽  
Author(s):  
YONGZHEN PEI ◽  
CHANGGUO LI ◽  
LANSUN CHEN ◽  
CHUNHUA WANG
Keyword(s):  
Biological Control ◽  
Control Strategy ◽  
Complex Dynamics ◽  
Impulsive Control ◽  
Critical Value ◽  
Asymptotically Stable ◽  
Behavior Dynamics ◽  
Impulsive Control Strategy ◽  
Predator Model ◽  
Predator System

This work investigates the dynamic behaviors of one-prey multi-predator model with defensive ability of the prey by introducing impulsive biological control strategy. By using the Floquent theorem and the small amplitude perturbation method, it is proved that there exists an asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value, and a permanence condition is established via the method of comparison involving multiple Liapunov functions. It is shown that the multi-predator impulsive control strategy is more effective than the classical one and makes the behavior dynamics of the system more complex.

scholarly journals An Impulsively Controlled Three-Species Prey-Predator Model with Stage Structure and Birth Pulse for Predator

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Yanyan Hu ◽  
Mei Yan ◽  
Zhongyi Xiang
Keyword(s):  
Small Amplitude ◽  
Floquet Theory ◽  
Stage Structure ◽  
Critical Value ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Birth Pulse ◽  
Impulsive Equation ◽  
Predator Model ◽  
Predator System

We investigate the dynamic behaviors of a two-prey one-predator system with stage structure and birth pulse for predator. By using the Floquet theory of linear periodic impulsive equation and small amplitude perturbation method, we show that there exists a globally asymptotically stable two-prey eradication periodic solution when the impulsive period is less than some critical value. Further, we study the permanence of the investigated model. Our results provide valuable strategy for biological economics management. Numerical analysis is also inserted to illustrate the results.

scholarly journals Impulsive Biological Pest Control Strategies of the Sugarcane Borer

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Marat Rafikov ◽  
Alfredo Del Sole Lordelo ◽  
Elvira Rafikova
Keyword(s):  
Pest Control ◽  
Floquet Theory ◽  
Control Strategies ◽  
Egg Parasitoid ◽  
Asymptotically Stable ◽  
Biological Pest Control ◽  
Globally Asymptotically Stable ◽  
Larval Stages ◽  
Sugarcane Borer ◽  
Impulsive Release

We propose an impulsive biological pest control of the sugarcane borer (Diatraea saccharalis) by its egg parasitoidTrichogramma galloibased on a mathematical model in which the sugarcane borer is represented by the egg and larval stages, and the parasitoid is considered in terms of the parasitized eggs. By using the Floquet theory and the small amplitude perturbation method, we show that there exists a globally asymptotically stable pest-eradication periodic solution when some conditions hold. The numerical simulations show that the impulsive release of parasitoids provides reliable strategies of the biological pest control of the sugarcane borer.

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