Modelling a single-species closed habitat fishery with spatial heterogeneity and time delay

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.

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A reaction–diffusion epidemic model with incubation period in almost periodic environments

European Journal of Applied Mathematics ◽

10.1017/s0956792520000303 ◽

2020 ◽

pp. 1-24

Author(s):

LIZHONG QIANG ◽

BIN-GUO WANG ◽

ZHI-CHENG WANG

Keyword(s):

Time Delay ◽

Spatial Heterogeneity ◽

Incubation Period ◽

Epidemic Model ◽

Reaction Diffusion ◽

Fixed Time ◽

Reaction Diffusion Equations ◽

Threshold Dynamics ◽

Almost Periodic ◽

Periodic Reaction

In this paper, we propose and study an almost periodic reaction–diffusion epidemic model in which disease latency, spatial heterogeneity and general seasonal fluctuations are incorporated. The model is given by a spatially nonlocal reaction–diffusion system with a fixed time delay. We first characterise the upper Lyapunov exponent $${\lambda ^*}$$ for a class of almost periodic reaction–diffusion equations with a fixed time delay and provide a numerical method to compute it. On this basis, the global threshold dynamics of this model is established in terms of $${\lambda ^*}$$ . It is shown that the disease-free almost periodic solution is globally attractive if $${\lambda ^*} < 0$$ , while the disease is persistent if $${\lambda ^*} < 0$$ . By virtue of numerical simulations, we investigate the effects of diffusion rate, incubation period and spatial heterogeneity on disease transmission.

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Permanence of a Single Species System with Distributed Time Delay and Feedback Control

Abstract and Applied Analysis ◽

10.1155/2012/867364 ◽

2012 ◽

Vol 2012 ◽

pp. 1-14 ◽

Cited By ~ 1

Author(s):

Yali Shen ◽

Fengqin Zhang ◽

Kai Wang

Keyword(s):

Time Delay ◽

Feedback Control ◽

Single Species ◽

Feedback Controls ◽

Distributed Time Delay

We study the permanence of a classofsingle species system with distributed time delay and feedback controls. General criteria on permanence are established in this paper. A very important fact is found in our results; that is, the feedback control is harmless to the permanence of species.

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Species-area relationships emerge from multiple coexistence mechanisms

10.1101/2021.04.02.438211 ◽

2021 ◽

Author(s):

David Garcia-Callejas ◽

Ignasi Bartomeus ◽

Oscar Godoy

Keyword(s):

Species Richness ◽

Spatial Heterogeneity ◽

Species Interactions ◽

Spatial Scales ◽

Single Species ◽

Small Population ◽

Collective Effects ◽

Demographic Stochasticity ◽

Species Dominance ◽

Species Area

The increase of species richness with area is a universal phenomenon on Earth. However, this observation contrasts with our poor understanding of how these species-area relationships (SARs) emerge from the collective effects of area, spatial heterogeneity, and local interactions. By combining a structuralist approach with five years of empirical observations in a highly-diverse grassland, we show that,contrary to expectations, spatial heterogeneity plays a little role in the accumulation of species richness with area in our system. Instead, as we increase the sampled area more species combinations are realized, and they coexist mainly due to direct pairwise interactions rather than by changes in single-species dominance or by indirect interactions. We also identify a small set of transient species with small population sizes that are consistently found across spatial scales. These findings empirically support the importance of the architecture of species interactions together with demographic stochasticity for driving SARs.

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Global stability of a single species model with feedback control and distributed time delay

Applied Mathematics and Computation ◽

10.1016/j.amc.2005.11.062 ◽

2006 ◽

Vol 178 (2) ◽

pp. 474-479 ◽

Cited By ~ 11

Author(s):

Fengde Chen

Keyword(s):

Time Delay ◽

Feedback Control ◽

Global Stability ◽

Single Species ◽

Distributed Time Delay ◽

Single Species Model

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A MODEL FOR THE EFFECT OF TIME DELAY ON THE DYNAMICS OF A POPULATION LIVING IN A POLLUTED ENVIRONMENT

Journal of Biological System ◽

10.1142/s0218339004001002 ◽

2004 ◽

Vol 12 (01) ◽

pp. 35-43 ◽

Cited By ~ 6

Author(s):

B. DUBEY

Keyword(s):

Mathematical Model ◽

Time Delay ◽

Single Species ◽

Polluted Environment ◽

Species Population ◽

Single Species Population

In this paper, a mathematical model is proposed and analyzed to study the effect of time delay on the dynamics of a single-species population living in a polluted environment. It is shown that time delay in the model has destabilizing effect on the system.

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Hopf Bifurcation in a Delayed Single Species Network System

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127421300081 ◽

2021 ◽

Vol 31 (03) ◽

pp. 2130008

Author(s):

Ranchao Wu ◽

Chuanying Zhang ◽

Zhaosheng Feng

Keyword(s):

Hopf Bifurcation ◽

Time Delay ◽

Continuous Time ◽

Single Species ◽

Discrete Space ◽

Network System ◽

Continuous Time Model ◽

Time Model ◽

Species Population ◽

Single Species Population

In this paper, we focus on a network system which describes spatiotemporal dynamics of single species population at different patches since species can have different features in various life stages and different behaviors in various spatial environments. With the effect of time delay and spatial dispersion, homogenous, periodic and spatiotemporally nonhomogeneous distributions are identified. The stability analysis is carried out for the discrete-space and continuous-time network on single species with time delay and the Hopf bifurcation of the single species population model in a network is explored. Formulas for determining the direction of Hopf bifurcation are derived by using the center manifold method and the normal form theorem. It is found that the network can generate spatial patterns only when time delay is present. Finally, numerical simulations are performed which agree well with our theoretical result, i.e. this discrete-space and continuous-time model admits regular temporal patterns since the delay induces Hopf bifurcations with network structure.

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