Non-linear waves in a ring of neurons

DOI10.1093/imamat/hxl002zbMath1117.37042OpenAlexW2065241324MaRDI QIDQ5297868

Shangjiang Guo, Li-Hong Huang

Publication date: 13 July 2007

Published in: IMA Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1093/imamat/hxl002

zbMATH Keywords

stabilityperiodic solutionsperiodic orbitspattern formationbasin of attractionartificial neural networkshomoclinic orbitscoupled delay differential equationsglobal continuation of wavesHopf bifuractionliving neurons systemssynaptic delay of signal transmission

Mathematics Subject Classification ID

Learning and adaptive systems in artificial intelligence (68T05) Neural biology (92C20) Dynamical systems in biology (37N25) Periodic orbits of vector fields and flows (37C27) Bifurcation theory of functional-differential equations (34K18)

Related Items (8)

Equivariant normal forms for parameterized delay differential equations with applications to bifurcation theory ⋮ Stability of nonlinear waves in a ring of neurons with delays ⋮ Dynamics of complex-valued fractional-order neural networks ⋮ Nonlinear dynamics and chaos in fractional-order neural networks ⋮ PATTERNS OF OSCILLATION IN A RING OF IDENTICAL CELLS WITH DELAYED COUPLING ⋮ Complex and chaotic dynamics in a discrete-time-delayed Hopfield neural network with ring architecture ⋮ PATTERN FORMATION IN A RING NETWORK WITH DELAY ⋮ Effects of asymmetric coupling and self-coupling on metastable dynamical transient rotating waves in a ring of sigmoidal neurons

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