Existence and global attractivity of positive almost periodic solutions for a kind of fishing model with pure-delay

summary:By using some analytical techniques, modified inequalities and Mawhin's continuation theorem of coincidence degree theory, some sufficient conditions for the existence of at least one positive almost periodic solution of a kind of fishing model with delay are obtained. Further, the global attractivity of the positive almost periodic solution of this model is also considered. Finally, three examples are given to illustrate the main results of this paper

Advanced Nonlinear Dynamics of Population Biology and Epidemiology

abstract: Modern biology and epidemiology have become more and more driven by the need of mathematical models and theory to elucidate general phenomena arising from the complexity of interactions on the numerous spatial, temporal, and hierarchical scales at which biological systems operate and diseases spread. Epidemic modeling and study of disease spread such as gonorrhea, HIV/AIDS, BSE, foot and mouth disease, measles, and rubella have had an impact on public health policy around the world which includes the United Kingdom, The Netherlands, Canada, and the United States. A wide variety of modeling approaches are involved in building up suitable models. Ordinary differential equation models, partial differential equation models, delay differential equation models, stochastic differential equation models, difference equation models, and nonautonomous models are examples of modeling approaches that are useful and capable of providing applicable strategies for the coexistence and conservation of endangered species, to prevent the overexploitation of natural resources, to control disease’s outbreak, and to make optimal dosing polices for the drug administration, and so forth.View the article as published at https://www.hindawi.com/journals/aaa/2014/214514

Modelling of a seasonally perturbed competitive three species impulsive system

The population of biological species in the ecosystem is known sensitive to the periodic fluctuations of seasonal change, food resources and climatic conditions. Research in the ecological management discipline conventionally models the behavior of such dynamic systems through specific impulsive response functions, but the results of such research are applicable only when the environments conform exactly to the conditions as defined by the specific response functions that have been implemented for specific scenarios. This means that the application of previous work may be somewhat limited. Moreover, the intra and inter competitions among species have been seldom studied for modelling the prey-predator ecosystem. To fill in the gaps this paper models the delicate balance of two-prey and one-predator system by addressing three main areas of: ⅰ) instead of using the specific impulse response this work models the ecosystem through a more general response function; ⅱ) to include the effects due to the competition between species and ⅲ) the system is subjected to the influences of seasonal factors. The seasonal factor has been implemented here in terms of periodic functions to represent the growth rates of predators. The sufficient condition for the local and global asymptotic stability of the prey-free periodic solution and the permanence of the system have been subsequently obtained by using the Comparison techniques and the Floquet theorems. Finally, the correctness of developed theories is verified by numerical simulation, and the corresponding biological explanation is given.2017005,2017019: Shanxi Agricultural University of Science and Technology Innovation Fund Projects

Mathematical Analysis for a Discrete Predator-Prey Model with Time Delay and Holling II Functional Response

This paper is concerned with a discrete predator-prey model with Holling II functional response and delays. Applying Gaines and Mawhin's continuation theorem of coincidence degree theory and the method of Lyapunov function, we obtain some sufficient conditions for the existence global asymptotic stability of positive periodic solutions of the model

Global Stability of Positive Periodic Solutions and Almost Periodic Solutions for a Discrete Competitive System

A discrete two-species competitive model is investigated. By using some preliminary lemmas and constructing a Lyapunov function, the existence and uniformly asymptotic stability of positive almost periodic solutions of the system are derived. In addition, an example and numerical simulations are presented to illustrate and substantiate the results of this paper

Pest and Pathogen Control: Strategic, Tactical, and Policy Models

This book describes mathematical models and systems analysis techniques applied to the study of insect pest, plant pathogens, and human diseases. The research programs of over 40 scientists from all over the world are compared and contrasted in detail to provide a state-of-the-art review on how such modeling can increase the effectiveness of more traditional ecological, biological, and chemical control methods. This is the first time such a synthesis has been attempted, and arises in part from a conference hosted by the International Institute for Applied Systems Analysis, Laxenburg, Austria. Papers from this event, plus additional solicited material, have been grouped by Professor Conway into three sections representing strategic, tactical, and policy decision models. An introduction and three linking chapters are provided to place these models in context. Discussing specific case histories in these mathematical terms and the consequent transfer of insights and methods will be of long-term interest to both professional and academic applied entomologists, plant pathologists, medical epidemiologists, applied ecologists, and systems analysts

Ecological stability theory : an analysis of method

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