Non-monotone cellular automata: Order prevails over chaos. (October 2022)

• Record Type: Journal Article
• Authors: Ekström, Henrik; Turova, Tatyana
• Is Part Of: Bio systems. Volume 220(2022)
• Publication Date: 2022-10
• Subjects: Cellular automata -- Integrate-and-fire neurons -- Non-monotone bootstrap percolation -- Spatio-temporal patterns; Biological systems -- Periodicals; Biology -- Periodicals; Biology -- Periodicals; Evolution -- Periodicals; Biologie -- Périodiques; Évolution -- Périodiques; 570
• DOI: 10.1016/j.biosystems.2022.104756
• Languages: English
• ISSNs: 0303-2647

Abstract

Abstract: We consider a model for the propagation of electrical impulses or activity in a neuronal network. The vertices of a square lattice represent neurons, and the edges of the lattice represent the synaptic connections. Each vertex v is assigned a type: inhibitory or excitatory. The dynamics of propagation of the initial activity captures features of the "integrate-and-fire" model. We study the spread of activation in a large network and describe possible spatio-temporal limiting patterns depending on the initial activation. The rich palette of the limits with qualitatively different properties, including expanding patterns, fixed patterns, and patterns moving across the network, allows us to argue that this is a versatile model for the study of associative memory.