scholarly journals On the Existence of Periodic Solutions of a Neutral Delay Model of Single-Species Population Growth

2001 ◽  
Vol 259 (1) ◽  
pp. 8-17 ◽  
Author(s):  
Fang Hui ◽  
Li Jibin
Keyword(s):  
Population Growth ◽  
Periodic Solutions ◽  
Single Species ◽  
Delay Model ◽  
Neutral Delay ◽  
Species Population ◽  
Existence Of Periodic Solutions ◽  
Single Species Population

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 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.

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.

The dynamics of collembolan populations: a matrix model of single species population growth

1977 ◽  
Vol 55 (2) ◽  
pp. 314-324 ◽  
Author(s):  
Barry C. Longstaff
Keyword(s):  
Population Growth ◽  
Matrix Model ◽  
Size Structure ◽  
Single Species ◽  
Deterministic Models ◽  
Damped Oscillations ◽  
Species Population ◽  
Population Sizes ◽  
Set Up ◽  
Single Species Population

The construction of a matrix model for the growth of populations of soil Collembola is described. Data from four replicate cultures of each of two species kept under laboratory conditions were modelled in the form of difference equations, which took into account the size structure of the populations. These equations were set up so as to effect a Leslie-type matrix model. The effect of density upon population growth rate was incorporated into the model in the form of a density-related function for fecundity.The success of the modelling procedures was varied with some of the models accurately predicting both the pattern of population growth and the population sizes at successive time intervals, whilst others only showed the trends. The deterministic models of each of the replicates for each species were combined to produce a stochastic model for that species. These also met with mixed success. The equilibrium values for the deterministic models were calculated and their stability properties examined. The models for both species predict a stable equilibrium approached by a series of damped oscillations.

scholarly journals A white-box model of population growth

2014 ◽  
Author(s):  
Lev V. Kalmykov ◽  
Vyacheslav L. Kalmykov
Keyword(s):  
Complex System ◽  
Population Dynamics ◽  
Complex Systems ◽  
Population Growth ◽  
Single Species ◽  
Black Box ◽  
Box Model ◽  
Holistic Approaches ◽  
Species Population ◽  
Single Species Population

Background. Integration of reductionist and holistic approaches is one of the great challenges for mathematical modeling. Mathematical models of complex systems are divided into black-box, white-box and grey-box types. A black-box model is completely nonmechanistic as internal mechanisms of a modeled complex system are hidden. A white-box model demonstrates direct mechanisms of functioning of a complex system. It holistically shows all events at microlevel, mesolevel and macrolevel of a modeled system at all stages of its dynamics. Earlier we have used the white-box modeling for verification and reformulation of the competitive exlusion principle. Here we investigate our white-box model of single-species population dynamics. This is fundamentally important because most basic ecological models are of black-box type, including Malthusian, Verhulst, Lotka-Volterra models. Methods. Our white-box model of single-species population growth is a purely logical deterministic individual-based cellular automata model. A biological prototype of the model is a vegetative propagation of rhizomatous lawn grasses. Using the Monte Carlo method, we investigate a role of different initial positioning of an individual in the habitat. We also investigate different size and structure of the habitat and two types of fecundity. Results. We have created and investigated a logical white-box model of an ecosystem with one species. This model demonstrates mechanisms of the S-shaped and double S-shaped population growth. We have investigated population growth limited by different factors, in particular by resources, habitat structure, intraspecific competition, lifetime of individuals, regeneration time and fecundity of individuals. We have compared the S-shaped curves with J-shaped curves of population growth. Conclusion. We present a basic white-box model of population dynamics which combines reductionist and holistic approaches. Integration of reductionist and holistic approaches is provided by the simultaneous modeling of both part-whole and cause-effect relations in complex system. We consider this holystic multi-level white-box modeling approach as a method of artificial intelligence which works as hyper-logical automatic deductive inference that provides direct mechanistic insights into complex systems. The white-box modeling by logical deterministic cellular automata is a perspective way for investigation not only of population dynamics but also of any complex systems.

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