Journal ArticleDOI
Herd behavior in a predator–prey model with spatial diffusion: bifurcation analysis and Turing instability
TLDR
In this article, the authors considered an ecological model, in a predator-prey interaction with the presence of a herd behavior, and proved the existence of positive solution and also the existence Hopf bifurcation, Turing driven instability, and Turing hopf point.Abstract:
We consider in this paper an ecological model, in a predator–prey interaction with the presence of a herd behavior. For the analysis of the model, the existence of positive solution and also the existence Hopf bifurcation, Turing driven instability, and Turing–Hopf bifurcation point have bee proved. Then by calculating the normal form, on the center of the manifold associated to the Hopf bifurcation points, the stability of the periodic solution has been proved. In the last part of the paper, numerical simulations has been given to illustrate our theoretical analysis.read more
Citations
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Journal ArticleDOI
Mathematical and numerical analysis of a three‐species predator‐prey model with herd behavior and time fractional‐order derivative
Journal ArticleDOI
Mathematical analysis of a fractional-order predator-prey model with prey social behavior and infection developed in predator population
TL;DR: In this article, a variety of fractional predator-prey models in the presence of an infection developed in the predator population were considered and the local behavior of the equilibrium points, and the existence of Hopf bifurcation were obtained.
Journal ArticleDOI
On approximate solutions for a fractional prey–predator model involving the Atangana–Baleanu derivative
Behzad Ghanbari,Behzad Ghanbari +1 more
TL;DR: In this paper, the Atangana-Baleanu fractional derivative is used to describe the rate of evolution of functions in the model and an iterative method for determining the numerical solution of fractional systems has been developed.
Journal ArticleDOI
Impact of prey herd shape on the predator-prey interaction
TL;DR: In this article, a delayed predator-prey model with the presence of a social behavior for the prey population has been investigated and a new functional response is obtained, where the effect of the herd shape for the predator population on the prey and predator equilibrium densities is studied.
Journal ArticleDOI
The influence of an infectious disease on a prey-predator model equipped with a fractional-order derivative
TL;DR: In this paper, the influence of an infectious disease in the evolution of ecological species is discussed, where a computational predator-prey model of fractional order is considered and the stability of equilibrium points is studied.
References
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Book
Introduction to Applied Nonlinear Dynamical Systems and Chaos
TL;DR: The Poincare-Bendixson Theorem as mentioned in this paper describes the existence, uniqueness, differentiability, and flow properties of vector fields, and is used to prove that a dynamical system is Chaotic.
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).
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Methods of Bifurcation Theory
Shui-Nee Chow,Jack K. Hale +1 more
TL;DR: In this paper, the static and dynamic aspects of bifurcation theory, which are of particular pertinence to differential equations, have been discussed, and a discussion of the changes that occur in the structure of the set of zeros of a function as parameters in the function are varied.
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Theory and Applications of Partial Functional Differential Equations
TL;DR: In this paper, the existence and compactness of solution semiflows of linear systems are investigated. But the authors focus on the nonhomogeneous systems and do not consider the linearized stability of non-homogeneous solutions.
Journal ArticleDOI
Mutual interference between parasites or predators and its effect on searching efficiency
TL;DR: A number of experiments indicate that a basic assumption implicit in early population models of predator-prey and parasite-host interactions is false.