Geodesic
Modality analysis of patterns in reaction-diffusion systems with random perturbations
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 53 (2019), pp. 73-82

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In this paper, a distributed Brusselator model with diffusion is investigated. It is well known that this model undergoes both Andronov–Hopf and Turing bifurcations. It is shown that in the parametric zone of diffusion instability the model generates a variety of stable spatially nonhomogeneous structures (patterns). This system exhibits a phenomenon of the multistability with the diversity of stable spatial structures. At the same time, each pattern has its unique parametric range, on which it may be observed. The focus is on analysis of stochastic phenomena of pattern formation and transitions induced by small random perturbations. Stochastic effects are studied by the spatial modality analysis. It is shown that the structures possess different degrees of stochastic sensitivity.
Keywords: Turing instability, self-organization, pattern formation, noise-induced dynamics, modality analysis.
Mots-clés : reaction-diffusion model 
@article{IIMI_2019_53_a6,
     author = {A. P. Kolinichenko and L. B. Ryashko},
     title = {Modality analysis of patterns in reaction-diffusion systems with random perturbations},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {73--82},
     publisher = {mathdoc},
     volume = {53},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2019_53_a6/}
}
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A. P. Kolinichenko; L. B. Ryashko. Modality analysis of patterns in reaction-diffusion systems with random perturbations. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 53 (2019), pp. 73-82. http://geodesic.mathdoc.fr/item/IIMI_2019_53_a6/