scholarly journals Two Positive Periodic Solutions for a Neutral Delay Model of Single-Species Population Growth with Harvesting

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Hui Fang
Keyword(s):  
Population Growth ◽  
Periodic Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Single Species ◽  
Delay Model ◽  
Positive Periodic Solutions ◽  
Neutral Delay ◽  
Species Population ◽  
Single Species Population

By coincidence degree theory fork-set-contractive mapping, this paper establishes a new criterion for the existence of at least two positive periodic solutions for a neutral delay model of single-species population growth with harvesting. An example is given to illustrate the effectiveness of the result.

scholarly journals Permanence and Positive Periodic Solutions of a Discrete Delay Competitive System

2010 ◽  
Vol 2010 ◽  
pp. 1-22 ◽  
Author(s):  
Wenjie Qin ◽  
Zhijun Liu
Keyword(s):  
Periodic Solutions ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Discrete Delay ◽  
Positive Periodic Solutions ◽  
Competitive System ◽  
Discrete Function ◽  
Species Population

A discrete time non-autonomous two-species competitive system with delays is proposed, which involves the influence of many generations on the density of species population. Sufficient conditions for permanence of the system are given. When the system is periodic, by using the continuous theorem of coincidence degree theory and constructing a suitable Lyapunov discrete function, sufficient conditions which guarantee the existence and global attractivity of positive periodic solutions are obtained. As an application, examples and their numerical simulations are presented to illustrate the feasibility of our main results.

scholarly journals Dynamics of a Single Species in a Fluctuating Environment under Periodic Yield Harvesting

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Mustafa Hasanbulli ◽  
Svitlana P. Rogovchenko ◽  
Yuriy V. Rogovchenko
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Blow Up ◽  
Single Species ◽  
Bifurcation Parameter ◽  
Positive Periodic Solutions ◽  
Large Initial Data ◽  
Fluctuating Environment ◽  
Species Population ◽  
Single Species Population

We discuss the effect of a periodic yield harvesting on a single species population whose dynamics in a fluctuating environment is described by the logistic differential equation with periodic coefficients. This problem was studied by Brauer and Sánchez (2003) who attempted the proof of the existence of two positive periodic solutions; the flaw in their argument is corrected. We obtain estimates for positive attracting and repelling periodic solutions and describe behavior of other solutions. Extinction and blow-up times are evaluated for solutions with small and large initial data; dependence of the number of periodic solutions on the parameterσassociated with the intensity of harvesting is explored. Asσgrows, the number of periodic solutions drops from two to zero. We provide bounds for the bifurcation parameter whose value in practice can be efficiently approximated numerically.

scholarly journals Positive Periodic Solutions for Neutral Delay Ratio-Dependent Predator-Prey Model with Holling-Tanner Functional Response

2011 ◽  
Vol 2011 ◽  
pp. 1-14
Author(s):  
Guirong Liu ◽  
Sanhu Wang ◽  
Jurang Yan
Keyword(s):  
Periodic Solutions ◽  
Functional Response ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solutions ◽  
Neutral Delay ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent

By using a continuation theorem based on coincidence degree theory, we establish some easily verifiable criteria for the existence of positive periodic solutions for neutral delay ratio-dependent predator-prey model with Holling-Tanner functional responsex'(t)=x(t)[r(t)-a(t)x(t-σ(t))-b(t)x'(t-σ(t))]-c(t)x(t)y(t)/h(t)y(t)+x(t),y'(t)=y(t)d(t)-f(t)y(t-τ(t))/x(t-τ(t)).

Population growth and density dependence

2019 ◽  
pp. 63-80
Author(s):  
Gary G. Mittelbach ◽  
Brian J. McGill
Keyword(s):  
Population Growth ◽  
Density Dependence ◽  
Growth Model ◽  
Species Interactions ◽  
Single Species ◽  
Positive Density ◽  
Allee Effects ◽  
Species Population ◽  
Exponential Growth Model ◽  
Single Species Population

This chapter reviews the basic mathematics of population growth as described by the exponential growth model and the logistic growth model. These simple models of population growth provide a foundation for the development of more complex models of species interactions covered in later chapters on predation, competition, and mutualism. The second half of the chapter examines the important topic of density-dependence and its role in population regulation. The preponderance of evidence for negative density-dependence in nature is reviewed, along with examples of positive density dependence (Allee effects). The study of density dependence in single-species populations leads naturally to the concept of community-level regulation, the idea that species richness or the total abundance of individuals in a community may be regulated just like abundance in a single-species population. The chapter concludes with a look at the evidence for community regulation in nature and a discussion of its importance.

scholarly journals Positive Periodic Solutions of Cooperative Systems with Delays and Feedback Controls

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Tursuneli Niyaz ◽  
Ahmadjan Muhammadhaji
Keyword(s):  
Periodic Solutions ◽  
Continuous Time ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Positive Periodic Solutions ◽  
Feedback Controls ◽  
Volterra Systems

This paper studies a class of periodicnspecies cooperative Lotka-Volterra systems with continuous time delays and feedback controls. Based on the continuation theorem of the coincidence degree theory developed by Gaines and Mawhin, some new sufficient conditions on the existence of positive periodic solutions are established.

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