Synchrony in networks of coupled non-smooth dynamical systems: Extending the master stability function

DOI10.1017/S0956792516000115zbMath1384.34064OpenAlexW2313042012MaRDI QIDQ4594618

Rüdiger Thul, Stephen Coombes

Publication date: 24 November 2017

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

Full work available at URL: https://doi.org/10.1017/s0956792516000115

zbMATH Keywords

neural networkscomplex networkssynchronisationnon-smooth equationsgeneral applied mathematics

Mathematics Subject Classification ID

Neural networks for/in biological studies, artificial life and related topics (92B20) Bifurcation theory for ordinary differential equations (34C23) Discontinuous ordinary differential equations (34A36) Synchronization of solutions to ordinary differential equations (34D06)

Related Items

Twenty Hopf-like bifurcations in piecewise-smooth dynamical systems ⋮ Convergence and synchronization in networks of piecewise-smooth systems via distributed discontinuous coupling ⋮ Network analysis and modelling: Special issue ofEuropean Journal of Applied Mathematics ⋮ Master stability function for piecewise smooth Filippov networks ⋮ Discontinuity-induced intermittent synchronization transitions in coupled non-smooth systems ⋮ Necessary Conditions for Complete Synchronization of a Coupled Chaotic Aihara Neuron Network with Electrical Synapses ⋮ Networks of piecewise linear neural mass models ⋮ The infinitesimal phase response curves of oscillators in piecewise smooth dynamical systems ⋮ Periodic Orbits and Chaos in Nonsmooth Delay Differential Equations ⋮ Recent advances in coupled oscillator theory ⋮ The two-process model for sleep-wake regulation: a nonsmooth dynamics perspective

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Mathematical frameworks for oscillatory network dynamics in neuroscience
• Andronov-Hopf bifurcations in planar, piecewise-smooth, continuous flows
• Synchronization processes in complex networks
• Dynamical systems on networks. A tutorial
• Bifurcation of periodic orbits in a class of planar Filippov systems
• Nonsmooth modeling and simulation for switched circuits.
• Semi-passivity and synchronization of diffusively coupled neuronal oscillators
• Local analysis of \(C\)-bifurcations in \(n\)-dimensional piecewise-smooth dynamical systems
• Weakly connected neural networks
• Mixed-mode oscillations in a stochastic, piecewise-linear system
• Homoclinic bifurcations in planar piecewise-linear systems
• Piecewise-smooth dynamical systems. Theory and applications
• Scientific heritage of L. P. Shilnikov
• Nagumo's equation
• BIFURCATIONS IN A STAR-LIKE NETWORK OF STUART–LANDAU OSCILLATORS
• Limit Cycles Bifurcating from the Periodic Orbits of a Discontinuous Piecewise Linear Differentiable Center with Two Zones
• Bifurcations in Nonsmooth Dynamical Systems
• Neuronal Networks with Gap Junctions: A Study of Piecewise Linear Planar Neuron Models
• Impact oscillators
• The McKean's Caricature of the Fitzhugh--Nagumo Model I. The Space-Clamped System
• Large-Amplitude Periodic Oscillations in Suspension Bridges: Some New Connections with Nonlinear Analysis
• Understanding cardiac alternans: A piecewise linear modeling framework
• Bifurcations in the Wilson--Cowan Equations with Nonsmooth Firing Rate
• Networks
• Symmetry in complex networks
• Bifurcations in nonlinear discontinuous systems

This page was built for publication: Synchrony in networks of coupled non-smooth dynamical systems: Extending the master stability function