Dynamics of Mutualism‐Competition‐Predator System with Beddington‐DeAngelis Functional Responses and  Impulsive Perturbations

Fan, Xiaoming; Wang, Zhigang; Jiang, Fuquan

doi:10.1155/2012/963486

Cited by 3 publications

(1 citation statement)

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“…These works have introduced the theory of impulsive differential equations and its applications and provided a theoretical basis of the application of impulsive differential equations. In recent years, Fan et al [22] have proposed the dynamics of a class of mutualismcompetition-predator interaction models with Beddington-DeAngelis functional responses and impulsive perturbations; this work is important for solving the global stability and the globally exponential stability of system. Yu and Lu [23] mainly focused on the permanence and global attractivity of a discrete almost periodic ratio-dependent Leslie system with time delays and feedback controls; these works vigorously promote the application of feedback control.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Mathematics and Sustainability in an Impulsive Eutrophication Controlling System

Zhao

Wang

2013

Abstract and Applied Analysis

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Eutrophication removal problems have captured the attention of biologists, mathematicians, and environmental scientists. Within this framework, an impulsive eutrophication controlling system is studied analytically and numerically. A key advantage of the eutrophication system is that it can be quite accurate to describe the interaction effect of some critical factors (fishermen catch and releasing small fry, etc.), which enables a systematic and logical procedure for fitting eutrophication mathematical system to real monitoring data and experiment data. Mathematical theoretical works have been pursuing the investigation of two threshold functions of some critical parameters under the condition of all species persistence, which can in turn provide a theoretical basis for the numerical simulation. Using numerical simulation works, we mainly focus on how to choose the best value of some critical parameters to ensure the sustainability of the eutrophication system so that the eutrophication removal process can be well developed with maximizing economic benefit. These results may be further extended to provide a basis for simulating the algal bloom in the laboratory and understanding the application of some impulsive controlling models about eutrophication removal problems.

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Section: Introductionmentioning

confidence: 99%