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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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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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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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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-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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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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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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Backward Parabolicity, Cross-Diffusion and Turing Instability [PDF]
Journal of Nonlinear Science, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Moussa, Ayman +2 more
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Emergence of Geometric Turing Patterns in Complex Networks
Physical Review X, 2023 Turing patterns, arising from the interplay between competing species of diffusive particles, have long been an important concept for describing nonequilibrium self-organization in nature and have been extensively investigated in many chemical and ...
Jasper van der Kolk +4 more
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