Effects of small world connection on the dynamics of a delayed ring network

DOI10.1007/S11071-008-9384-9zbMath1169.92006OpenAlexW2015936883MaRDI QIDQ840555

Xu Xu, Zaihua Wang

Publication date: 11 September 2009

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-008-9384-9

zbMATH Keywords

chaosbifurcationglobal stability

Mathematics Subject Classification ID

Learning and adaptive systems in artificial intelligence (68T05) Dynamical systems in biology (37N25) Neural networks for/in biological studies, artificial life and related topics (92B20) Asymptotic theory of functional-differential equations (34K25) Stability theory of functional-differential equations (34K20) Periodic solutions to functional-differential equations (34K13) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Qualitative investigation and simulation of models involving functional-differential equations (34K60)

Related Items (14)

STABILITY AND BIFURCATION FOR A CLASS OF TRI-NEURON NETWORKS WITH BIDIRECTIONALLY DELAYED CONNECTIONS AND SELF-FEEDBACK ⋮ Stability and instability of a neuron network with excitatory and inhibitory small-world connections ⋮ Hidden extreme multistability with hyperchaos and transient chaos in a Hopfield neural network affected by electromagnetic radiation ⋮ Stability switches, bifurcation, and multi-stability of coupled networks with time delays ⋮ Exponential stability and spectral analysis of a delayed ring neural network with a small-world connection ⋮ Stability and Hopf bifurcation analysis of a pair of three-neuron loops with time delays ⋮ A novel deterministic hybrid complex network model created by inner-outer iteration ⋮ Quasiperiodicity and Chaos Through Hopf–Hopf Bifurcation in Minimal Ring Neural Oscillators Due to a Single Shortcut ⋮ DYNAMICS IN TIME-DELAY RECURRENTLY COUPLED OSCILLATORS ⋮ COLLECTIVE DYNAMICS AND CONTROL OF A 3-D SMALL-WORLD NETWORK WITH TIME DELAYS ⋮ Wave propagation and synchronization induced by chemical autapse in chain Hindmarsh-Rose neural network ⋮ Stabilization of metastable dynamical rotating waves in a ring of unidirectionally coupled sigmoidal neurons due to shortcuts ⋮ Induction of Hopf bifurcation and oscillation death by delays in coupled networks ⋮ EFFECTS OF SHORT-CUT IN A DELAYED RING NETWORK

Uses Software

• XPPAUT

Cites Work

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• Complex networks: structure and dynamics
• Symmetric functional differential equations and neural networks with memory
• DYNAMICS OF A TWO-DIMENSIONAL DELAYED SMALL-WORLD NETWORK UNDER DELAYED FEEDBACK CONTROL
• Collective dynamics of ‘small-world’ networks
• Complicated dynamics of a ring neural network with time delays
• Equivariant Hopf bifurcation in a ring of identical cells with delayed coupling
• Fractals in small-world networks with time-delay

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