Existence and stability of a synchronous oscillation in a neural system with delayed coupling

DOI10.1016/J.JMAA.2013.11.031zbMath1317.34154OpenAlexW1983196212MaRDI QIDQ2019178

Israel Ncube

Publication date: 27 March 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2013.11.031

zbMATH Keywords

criticalityHopf bifurcationnormal formdelay differential equationsexistence and uniquenesscentre manifold

Mathematics Subject Classification ID

Transformation and reduction of functional-differential equations and systems, normal forms (34K17) Stability theory of functional-differential equations (34K20) Periodic solutions to functional-differential equations (34K13) Bifurcation theory of functional-differential equations (34K18) Invariant manifolds of functional-differential equations (34K19) Stationary solutions of functional-differential equations (34K21)

Cites Work

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• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Introduction to functional differential equations
• Synchronization and stable phase-locking in a network of neurons with memory.
• Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation
• Normal forms for retarded functional differential equations and applications to Bogdanov-Takens singularity
• Multistability and stable asynchronous periodic oscillations in a multiple-delayed neural system
• Synchronized Hopf bifurcation analysis in a neural network model with delays
• PATTERNS OF OSCILLATION IN A RING OF IDENTICAL CELLS WITH DELAYED COUPLING
• Flows on centre manifolds for scalar functional differential equations
• Stability and Bifurcations of Equilibria in a Multiple-Delayed Differential Equation
• Stability, Bifurcation, and Multistability in a System of Two Coupled Neurons with Multiple Time Delays
• Equivariant Hopf bifurcation in a ring of identical cells with delayed coupling

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