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Turing instabilities for three interacting species
Applied Mathematics LettersIn this paper, I prove necessary and sufficient conditions for the existence of Turing instabilities in a general system with three interacting species. Turing instabilities describe situations when a stable steady state of a reaction system (ordinary differential equation) becomes an unstable homogeneous steady state of the corresponding reaction ...
Piskovsky, Vit
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A Nonlinear Cross-Diffusion Model for Disease Spread: Turing Instability and Pattern Formation
MathematicsIn this article, we propose a novel nonlinear cross-diffusion framework to model the distribution of susceptible and infected individuals within their habitat using a reduced SIR model that incorporates saturated incidence and treatment rates.
Ravi P. Gupta +2 more
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From Turing Instability to Fractals [PDF]
Nonlinear Photonics, 2007 Complexity focuses on commonality across subject areas and forms a natural platform for multidisciplinary activities. Typical generic signatures of complexity include: (i) spontaneous occurrence of simple patterns (e.g. stripes, squares, hexagons) emerging as dominant nonlinear modes [1], and (ii) the formation of a highly complex pattern in the form ...
Huang, JG +4 more
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Turing instability for a Leslie–Gower model
Ricerche di Matematica, 2023 Abstract The aim of this paper is to investigate a reaction-diffusion Leslie–Gower predator–prey model, incorporating the intraguild predation and both self and cross-diffusion. The longtime behaviour of the solutions is analysed, proving the existence of an absorbing set.
Capone F. +4 more
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Turing instabilities on Cartesian product networks [PDF]
Scientific Reports, 2015 AbstractThe problem of Turing instabilities for a reaction-diffusion system defined on a complex Cartesian product network is considered. To this end we operate in the linear regime and expand the time dependent perturbation on a basis formed by the tensor product of the eigenvectors of the discrete Laplacian operators, associated to each of the ...
ASLLANI, MALBOR +4 more
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Turing instability in a boundary-fed system [PDF]
Physical Review E, 1998 41 pages, 18 figures, to be published in Physical Review ...
Setayeshgar, S., Cross, M. C.
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Hopf bifurcation and Turing instability in a diffusive predator-prey model with hunting cooperation
Open Mathematics, 2022 In this article, we study Hopf bifurcation and Turing instability of a diffusive predator-prey model with hunting cooperation. For the local model, we analyze the stability of the equilibrium and derive conditions for determining the direction of Hopf ...
Miao Liangying, He Zhiqian
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Boundary Value Problems, 2022 In this paper, a modified cross-diffusion Leslie–Gower predator–prey model with the Beddington–DeAngelis functional response is studied. We use the linear stability analysis on constant steady states to obtain sufficient conditions for the occurrence of ...
Marzieh Farshid, Yaghoub Jalilian
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Discrete Dynamics in Nature and Society, 2022 A delayed diffusive predator-prey model with predator interference or foraging facilitation is studied. We are interested in the existence of Turing instability, local stability, and Hopf bifurcation. We analyze the direction and stability of bifurcating
Wenlong Wang, Zijun Liu, Ruizhi Yang
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Turing instability in the one-parameter Gierer–Meinhardt system [PDF]
, 2023 The purpose of this work is to find the region of necessary and sufficient conditions for diffusion instability on the parameter plane (τ, d) of the Gierer–Meinhardt system, where τ is the relaxation parameter, d is the dimensionless ...
Ryabov, Anatoly Сергеевич +1 more
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