The bifurcation study of 1:2 resonance in a delayed system of two coupled neurons

DOI10.1007/s10884-012-9279-9zbMath1279.34084OpenAlexW1976081455MaRDI QIDQ1949243

Guihong Fan, Gail S. K. Wolkowicz, Sue Ann Campbell, Huai-Ping Zhu

Publication date: 6 May 2013

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-012-9279-9

zbMATH Keywords

delayHopf bifurcationnormal formhomoclinic orbitcenter manifoldBogdanov-Takens bifurcationneuron1:2 resonanceuniversal unfolding

Mathematics Subject Classification ID

Neural networks for/in biological studies, artificial life and related topics (92B20) Transformation and reduction of functional-differential equations and systems, normal forms (34K17) Stability theory of functional-differential equations (34K20) Bifurcation theory of functional-differential equations (34K18) Invariant manifolds of functional-differential equations (34K19)

Related Items (10)

The Bogdanov-Takens bifurcation study of \(2m\) coupled neurons system with \(2m+1\) delays ⋮ Canard explosion in delay differential equations ⋮ Hopf Bifurcation Analysis of Distributed Delay Equations with Applications to Neural Networks ⋮ Codimension-Two Bifurcations and Bifurcation Controls in a Discrete Biological System with Weak Allee Effect ⋮ Bogdanov-Takens bifurcation with \(Z_2\) symmetry and spatiotemporal dynamics in diffusive Rosenzweig-MacArthur model involving nonlocal prey competition ⋮ Persistence and smooth dependence on parameters of periodic orbits in functional differential equations close to an ODE or an evolutionary PDE ⋮ Resonance Phenomena in a Scalar Delay Differential Equation with Two State-Dependent Delays ⋮ Bogdanov–Takens and Triple Zero Bifurcations of Coupled van der Pol–Duffing Oscillators with Multiple Delays ⋮ Codimension one and two bifurcations of a discrete stage-structured population model with self-limitation ⋮ Bogdanov–Takens and triple zero bifurcations in general differential systems with m delays

Uses Software

• Maple

Cites Work

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