Dynamics and bifurcations of a discrete-time prey-predator model with Allee effect on the prey population

We derive and study a Darwinian dynamic model based on a low-dimensional discrete- time population model focused on two features: density-dependent fertility and a trade-off between inherent (density free) fertility and post-reproduction survival. Both features are assumed to be dependent on a phenotypic trait subject to natural selection. The model tracks the dynamics of the population coupled with that of the population mean trait. We study the stability properties of equilibria by means of bifurcation theory. Whether post-reproduction survival at equilibrium is low or high is shown, in this model, to depend significantly on the nature of the trait dependence of the density effects. An Allee effect can also play a significant role.

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A PREY-PREDATOR MODEL WITH DIFFUSION AND A SUPPLEMENTARY RESOURCE FOR THE PREY IN A TWO‐PATCH ENVIRONMENT

Mathematical Modelling and Analysis ◽

10.3846/13926292.2004.9637238 ◽

2005 ◽

Vol 9 (1) ◽

pp. 9-24 ◽

Cited By ~ 9

Author(s):

J. Dhar

Keyword(s):

Steady State ◽

Asymptotic Stability ◽

Prey Species ◽

Steady State Solution ◽

State Solution ◽

Prey Population ◽

Predator Species ◽

Additional Resource ◽

Linear And Nonlinear ◽

Predator Model

In this paper, a prey‐predator dynamics, where the predator species partially depends upon the prey species, in a two patch habitat with diffusion and there is a non‐diffusing additional resource for the prey population, is modeled and analyzed. It is shown, that there exists a positive, monotonic, continuous steady state solution with continuous matching at the interface for both the species separately. Further, we obtain conditions for asymptotic stability for both linear and nonlinear cases. Šiame straipsnyje modeliuojama ir analizuojama plešr‐unu ir auku dinamika, laikant, kad plešr-unu populiacija dalinai priklauso nuo auku skačiaus. Areala sudaro dvi sritys, kuriose vyksta populiaciju individu difuzija, be to, aukoms yra išskirtas nedifunduojantis resursas. Irodyta, kad egzistuoja teigiamas, monotoniškas, tolydus stacionarusis sprendinys, tenkinantis tolydumo salyga abiems populiacijoms atskirai. Gautos asimptotinio stabilumo salygos tiesiniu ir netiesiniu atvejais.

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Stability, bifurcation, and chaos control of a novel discrete-time model involving Allee effect and cannibalism

Advances in Difference Equations ◽

10.1186/s13662-020-02838-z ◽

2020 ◽

Vol 2020 (1) ◽

Cited By ~ 1

Author(s):

Muhammad Sajjad Shabbir ◽

Qamar Din ◽

Khalil Ahmad ◽

Asifa Tassaddiq ◽

Atif Hassan Soori ◽

...

Keyword(s):

Discrete Time ◽

Chaos Control ◽

Allee Effect ◽

Bifurcation And Chaos ◽

Time Model ◽

Discrete Time Model

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Dynamical study of a prey–predator model incorporating nonlinear prey refuge and additive Allee effect acting on prey species

Modeling Earth Systems and Environment ◽

10.1007/s40808-020-01049-5 ◽

2020 ◽

Author(s):

Hafizul Molla ◽

Md. Sabiar Rahman ◽

Sahabuddin Sarwardi

Keyword(s):

Allee Effect ◽

Prey Species ◽

Prey Refuge ◽

Dynamical Study ◽

Predator Model

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DYNAMICAL STUDY OF DISCRETE-TIME PREY–PREDATOR MODEL WITH CONSTANT PREY REFUGE UNDER IMPRECISE BIOLOGICAL PARAMETERS

Journal of Biological System ◽

10.1142/s0218339020500114 ◽

2020 ◽

Vol 28 (03) ◽

pp. 681-699

Author(s):

P. K. SANTRA ◽

G. S. MAHAPATRA

Keyword(s):

Discrete Time ◽

Discrete Model ◽

Prey Species ◽

Complex Nature ◽

Biological Parameters ◽

Constant Number ◽

Prey Refuge ◽

Dynamical Study ◽

Dynamical Properties ◽

Predator Model

The objective of this paper is to study the dynamical properties of a discrete-time prey–predator model under imprecise biological parameters. We consider refuge for prey species as a constant number. The equilibria of the model are obtained, and the dynamic behaviors of the proposed system are examined for the interval biological parameters. Simulations of the model are performed for different parameters of the model. Numerical simulations demonstrate that the proposed discrete model exhibits rich dynamics of a chaotic and complex nature.

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