Extinction, stable pattern and their transition in a diffusive single species population with distributed maturity

2008 ◽  
Vol 19 (3) ◽  
pp. 285-309
Author(s):  
PEIXUAN WENG
Keyword(s):  
Distributed Delay ◽  
Reaction Diffusion ◽  
Single Species ◽  
Cylindrical Domain ◽  
Stable Pattern ◽  
Structured Population ◽  
Species Population ◽  
Single Species Population ◽  
Spatially Varying ◽  
Robin Boundary

We consider a single-species structured population with distributed maturity and spatial diffusion in a cylindrical domain subject to Neumann and Robin boundary conditions. We first establish the threshold property of the reaction–diffusion system with distributed delay and non-local interaction in a corresponding lower-dimensional domain, so that the system approaches either an extinction state or a stable spatially varying pattern. We then investigate the transition from the extinction state to the stable pattern of the system in the cylindrical domain.

scholarly journals Comparison principles for impulsive parabolic equations with applications to models of single species growth

1991 ◽  
Vol 32 (4) ◽  
pp. 382-400 ◽  
Author(s):  
L. H. Erbe ◽  
H. I. Freedman ◽  
X. Z. Liu ◽  
J. H. Wu
Keyword(s):  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Single Species ◽  
Reaction Diffusion Equation ◽  
Equation Modeling ◽  
Positive Equilibrium ◽  
Comparison Principles ◽  
Nonlinear Parabolic ◽  
Species Population ◽  
Single Species Population

AbstractThis paper establishes some maximum and comparison principles relative to lower and upper solutions of nonlinear parabolic partial differential equations with impulsive effects. These principles are applied to obtain some sufficient conditions for the global asymptotic stability of a unique positive equilibrium in a reaction-diffusion equation modeling the growth of a single-species population subject to abrupt changes of certain important system parameters.

scholarly journals Qualitative Analysis of a Single-Species Model with Distributed Delay and Nonlinear Harvest

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2560
Author(s):  
Zuxiong Li ◽  
Shengnan Fu ◽  
Huili Xiang ◽  
Hailing Wang
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Single Species ◽  
Dimensional System ◽  
Globally Asymptotically Stable ◽  
Species Population ◽  
Existence And Stability ◽  
Single Species Population

In this paper, a single-species population model with distributed delay and Michaelis-Menten type harvesting is established. Through an appropriate transformation, the mathematical model is converted into a two-dimensional system. Applying qualitative theory of ordinary differential equations, we obtain sufficient conditions for the stability of the equilibria of this system under three cases. The equilibrium A1 of system is globally asymptotically stable when br−c>0 and η<0. Using Poincare-Bendixson theorem, we determine the existence and stability of limit cycle when br−c>0 and η>0. By computing Lyapunov number, we obtain that a supercritical Hopf bifurcation occurs when η passes through 0. High order singularity of the system, such as saddle node, degenerate critical point, unstable node, saddle point, etc, is studied by the theory of ordinary differential equations. Numerical simulations are provided to verify our main results in this paper.

scholarly journals Survival analysis of a stochastic delay single-species system in polluted environment with psychological effect and pulse toxicant input

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiangjun Dai ◽  
Suli Wang ◽  
Weizhi Xiong ◽  
Ni Li
Keyword(s):  
Sufficient Conditions ◽  
Single Species ◽  
Threshold Value ◽  
Psychological Effect ◽  
Polluted Environment ◽  
Population System ◽  
Stochastic Delay ◽  
Species Population ◽  
The Mean ◽  
Single Species Population

Abstract We propose and study a stochastic delay single-species population system in polluted environment with psychological effect and pulse toxicant input. We establish sufficient conditions for the extinction, nonpersistence in the mean, weak persistence, and strong persistence of the single-species population and obtain the threshold value between extinction and weak persistence. Finally, we confirm the efficiency of the main results by numerical simulations.

scholarly journals STUDY OF SINGLE-SPECIES POPULATION MODELS

2020 ◽  
pp. 161-166
Author(s):  
Marthak Rutu
Keyword(s):  
Spatial Heterogeneity ◽  
Environmental Effects ◽  
Age Structure ◽  
Single Species ◽  
Research Paper ◽  
Population Models ◽  
Deterministic Models ◽  
One Dimensional ◽  
Species Population ◽  
Single Species Population

In this research paper one dimensional population models developed centuries ago shows that growth and/decay of single homogeneous populations But environmental effects spatial heterogeneity or age-structure deterministic models prevailing single species population models.

scholarly journals Coarse, Medium or Fine? A Quantum Mechanics Approach to Single Species Population Dynamics

2020 ◽  
Author(s):  
Olcay Akman ◽  
Leon Arriola ◽  
Aditi Ghosh ◽  
Ryan Schroeder
Keyword(s):  
Population Dynamics ◽  
Quantum Mechanics ◽  
Single Species ◽  
Stable Equilibrium Point ◽  
Ode Model ◽  
Deterministic Models ◽  
Species Population ◽  
Quantum Approach ◽  
Single Species Population ◽  
Quantum Framework

AbstractStandard heuristic mathematical models of population dynamics are often constructed using ordinary differential equations (ODEs). These deterministic models yield pre-dictable results which allow researchers to make informed recommendations on public policy. A common immigration, natural death, and fission ODE model is derived from a quantum mechanics view. This macroscopic ODE predicts that there is only one stable equilibrium point . We therefore presume that as t → ∞, the expected value should be . The quantum framework presented here yields the same standard ODE model, however with very unexpected quantum results, namely . The obvious questions are: why isn’t , why are the probabilities ≈ 0.37, and where is the missing probability of 0.26? The answer lies in quantum tunneling of probabilities. The goal of this paper is to study these tunneling effects that give specific predictions of the uncertainty in the population at the macroscopic level. These quantum effects open the possibility of searching for “black–swan” events. In other words, using the more sophisticated quantum approach, we may be able to make quantitative statements about rare events that have significant ramifications to the dynamical system.

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.

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