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• W2891390274 abstract "We investigate a critically-coupled chain of nonlinear oscillators, whose dynamics displays complex spatiotemporal patterns of activity, including regimes in which glider-like coherent excitations move about and interact. The units in the network are identical simple neural circuits whose dynamics is given by the Wilson-Cowan model and are arranged in space along a one-dimensional lattice with nearest neighbor interactions. The interactions follow an alternating sign rule, and hence the “synaptic matrix” M embodying them is tridiagonal antisymmetric and has purely imaginary (critical) eigenvalues. The model illustrates the interplay of two properties: circuits with a complex internal dynamics, such as multiple stable periodic solutions and period doubling bifurcations, and coupling with a “critical” synaptic matrix, i.e., having purely imaginary eigenvalues. In order to identify the dynamical underpinnings of these behaviors, we explored a discrete-time coupled-map lattice inspired by our system: the dynamics of the units is dictated by a chaotic map of the interval, and the interactions are given by allowing the critical coupling to act for a finite period τ, thus given by a unitary matrix U=exp⁡(τ2M). It is now explicit that such critical couplings are volume-preserving in the sense of Liouville’s theorem. We show that this map is also capable of producing a variety of complex spatiotemporal patterns including gliders, like our original chain of neural circuits. Our results suggest that if the units in isolation are capable of featuring multiple dynamical states, then local critical couplings lead to a wide variety of emergent spatiotemporal phenomena." @default.
• W2891390274 created "2018-09-27" @default.
• W2891390274 creator A5058682817 @default.
• W2891390274 creator A5087436159 @default.
• W2891390274 date "2018-09-01" @default.
• W2891390274 modified "2023-09-23" @default.
• W2891390274 title "Complex spatiotemporal behavior and coherent excitations in critically-coupled chains of neural circuits" @default.
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• W2891390274 doi "https://doi.org/10.1063/1.5011766" @default.
• W2891390274 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/30278628" @default.
• W2891390274 hasPublicationYear "2018" @default.
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