Results 21 to 30 of about 32,448 (189)
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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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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Turing instabilities in general systems
Journal of Mathematical Biology, 2000 We present necessary and sufficient conditions on the stability matrix of a general n(> or = 2)-dimensional reaction-diffusion system which guarantee that its uniform steady state can undergo a Turing bifurcation. The necessary (kinetic) condition, requiring that the system be composed of an unstable (or activator) and a stable (or inhibitor) subsystem,
Satnoianu, R, Menzinger, M, Maini, P
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Turing Instability of Brusselator in the Reaction-Diffusion Network
Complexity, 2020 Turing instability constitutes a universal paradigm for the spontaneous generation of spatially organized patterns, especially in a chemical reaction. In this paper, we investigated the pattern dynamics of Brusselator from the view of complex networks ...
Yansu Ji, Jianwei Shen
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Non-linear effects on Turing patterns: time oscillations and chaos. [PDF]
, 2012 We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space, produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence,
Aragón, J. L. +4 more
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Characterization of Turing diffusion-driven instability on evolving domains [PDF]
, 2012 In this paper we establish a general theoretical framework for Turing diffusion-driven instability for reaction-diffusion systems on time-dependent evolving domains.
A. Gierer +43 more
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Turing-like instabilities from a limit cycle [PDF]
Physical Review E, 2015 The Turing instability is a paradigmatic route to pattern formation in reaction-diffusion systems. Following a diffusion-driven instability, homogeneous fixed points can become unstable when subject to external perturbation. As a consequence, the system evolves towards a stationary, nonhomogeneous attractor.
CHALLENGER, JOSEPH +2 more
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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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Stationary localised patterns without Turing instability
Mathematical Methods in the Applied Sciences, 2022 Since the pioneering work of Turing, it has been known that diffusion can destablise a homogeneous solution that is stable in the underlying model in the absence of diffusion. The destabilisation of the homogeneous solutions leads to the generation of patterns.
Fahad Al Saadi +3 more
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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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