Dynamics of a diffusion reaction prey–predator model with delay in prey: Effects of delay and spatial components
TLDR
In this paper, the authors studied the complex dynamics of a Monod-Haldane-type predator-prey interaction model that incorporates: (1) a constant time delay in the prey growth; and (2) diffusion in both prey and predator.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 2018-05-15 and is currently open access. It has received 17 citations till now. The article focuses on the topics: Hopf bifurcation & Population.read more
Citations
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Effect of herd shape in a diffusive predator-prey model with time delay
TL;DR: In this article, the effect of the shape of herd behavior on the interaction between predator and prey was studied in the absence of spatial diffusion and the time delay, where the local stability of the equilibrium states, the existence of Hopf bifurcation have been investigated.
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Stability of Hopf-bifurcating limit cycles in a diffusion-driven prey-predator system with Allee effect and time delay.
Kalyan Manna,Malay Banerjee +1 more
TL;DR: The numerical simulation results reveal that the Hopf bifurcation can potentially lead to spatially homogeneous periodic in time distribution of the populations which will eventually settles to chaotic in space and time distribution for sufficiently large value of the time delay.
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Dynamic study of a predator-prey model with Allee effect and Holling type-I functional response
TL;DR: In this article, a prey-predator model with Allee effect and Holling type-I functional response is established, and its dynamical behaviors are studied in detail, and the existence, boundedness and stability of the model are qualitatively discussed.
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Turing patterns in a diffusive Holling–Tanner predator-prey model with an alternative food source for the predator
Claudio Arancibia-Ibarra,Claudio Arancibia-Ibarra,Michael Bode,José D. Flores,Graeme J. Pettet,Peter van Heijster,Peter van Heijster +6 more
TL;DR: From the result of the temporal model, regions in parameter space in which Turing instability in the spatio-temporal model is expected are identified and numerical evidence where the Turing instability leads to spatio/temporal periodic solutions is shown.
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Analysis of the Predator–Prey Interactions: A Stochastic Model Incorporating Disease Invasion
TL;DR: In this article, a mathematical system was developed to investigate the impacts of environmental noise and infectious diseases on predator-prey interactions, and the globally unique positive solution was confirmed by using conventional methods.
References
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The Chemical Basis of Morphogenesis
TL;DR: In this article, it is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis.
Book
Introduction to Functional Differential Equations
TL;DR: The present book builds upon the earlier work of J. Hale, "Theory of Functional Differential Equations" published in 1977 and attempts to maintain the spirit of that book and have retained approximately one-third of the material intact.
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Delay Differential Equations: With Applications in Population Dynamics
TL;DR: Delay Differential Equations as mentioned in this paper are a generalization of delay differential equations and have been used in a variety of applications in population dynamics, such as global stability for single species models and multi-species models.
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The functional response of predators to prey density and its role in mimicry and population regulation.
TL;DR: These are my lecture notes from CS681: Design and Analysis of Algo rithms, a one-semester graduate course I taught at Cornell for three consec utive fall semesters from '88 to.
Book
Theory and applications of Hopf bifurcation
TL;DR: The Hopf Bifurcation Theorum has been used in many applications, such as Differential Difference and Integro-differential Equations (by hand).