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2024 | OriginalPaper | Chapter

Edge of Chaos in Reaction-Diffusion System with Memristor Synapses

Authors : Angela Slavova, Ventsislav Ignatov

Published in: New Trends in the Applications of Differential Equations in Sciences

Publisher: Springer Nature Switzerland

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Abstract

In this paper principles of local activity theory will be presented for studying complex behavior of reaction-diffusion systems. For reaction-diffusion models, one can determine the domain of the cell parameters in order for the cells to be locally active, and thus potentially capable of exhibiting complexity. In the literature, the so called edge of chaos (EC) means a region in the parameter space of a dynamical system, where complex phenomena and information processing can emerge. In this paper edge of chaos domain will be determined for a reaction-diffusion model with memristor synapses. In our model each cell will be arranged on a two-dimensional square grid and will be connected to adjacent cells through coupling devices that mimic 2-D spatial diffusion and transmit the cell’s state to its neighboring cells. Numerical simulations will illustrate the obtained theoretical results.

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previous chapter Numerical Determination of Age-Dependent Coefficients in an Integro-Hyperbolic System of Honeybee Population Dynamics
next chapter Inverse Modelling of the Cellular Immune Response to SARS-CoV-2
Literature
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A. Adamatzky, L. Chua. Memristor Networks, Springer, 2014.
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A. Slavova. Cellular Neural Networks: Dynamics and Modeling, Kluwer Academic Publishers, 2003.
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A. Slavova, R. Tetzlaff. Edge of chaos in reaction diffusion CNN model. Open Mathematics, 15:1, 2017.
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S. Smale. A mathematical model of two cells via Turings equation. Lectures in Applied Mathematics, 6 (American Mathematical Society), 1526, 1974.
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Metadata
Title
Edge of Chaos in Reaction-Diffusion System with Memristor Synapses
Authors
Angela Slavova
Ventsislav Ignatov
Copyright Year
2024
Book
New Trends in the Applications of Differential Equations in Sciences

Print ISBN: 978-3-031-53211-5

Electronic ISBN: 978-3-031-53212-2

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-53212-2_36

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