Weakly connected neural networks
From MaRDI portal
Publication:1366659
zbMath0887.92003MaRDI QIDQ1366659
Eugene M. Izhikevich, Frank C. Hoppensteadt
Publication date: 14 September 1997
Published in: Applied Mathematical Sciences (Search for Journal in Brave)
Neural biology (92C20) Neural networks for/in biological studies, artificial life and related topics (92B20) Circuits, networks (94C99) Additive difference equations (39A10) Research exposition (monographs, survey articles) pertaining to biology (92-02) General theory for ordinary differential equations (34A99)
Related Items (only showing first 100 items - show all)
Spike-adding in parabolic bursters: the role of folded-saddle canards ⋮ Wilson-Cowan equations for neocortical dynamics ⋮ Mathematical frameworks for oscillatory network dynamics in neuroscience ⋮ Temperature compensation via cooperative stability in protein degradation ⋮ The role of extracellular potassium dynamics in the different stages of ictal bursting and spreading depression: A computational study ⋮ A phase model with large time delayed coupling ⋮ The role of phase shifts of sensory inputs in walking revealed by means of phase reduction ⋮ Stability switches and multistability coexistence in a delay-coupled neural oscillators system ⋮ Oscillatory associative memory network with perfect retrieval ⋮ The mean field analysis of the Kuramoto model on graphs. I: The mean field equation and transition point formulas ⋮ Nonlinear dynamics and chaos methods in neurodynamics and complex data analysis ⋮ Phase resetting reduces theta-gamma rhythmic interaction to a one-dimensional map ⋮ On synchronization of networks of Wilson-Cowan oscillators with diffusive coupling ⋮ Phase response approaches to neural activity models with distributed delay ⋮ Mean-return-time phase of a stochastic oscillator provides an approximate renewal description for the associated point process ⋮ Stability switches and bifurcation in a system of four coupled neural networks with multiple time delays ⋮ Stability, bifurcation, and synchronization of delay-coupled ring neural networks ⋮ Bistability, bifurcations and chaos in the Mackey-Glass equation ⋮ Network architecture and spatio-temporally symmetric dynamics ⋮ Subtle noise structures as control signals in high-order biocognition ⋮ Bursting oscillations, bifurcation and synchronization in neuronal systems ⋮ Extreme phase sensitivity in systems with fractal isochrons ⋮ Spike width and frequency alter stability of phase-locking in electrically coupled neurons ⋮ Codimension-2 parameter space structure of continuous-time recurrent neural networks ⋮ Integrate and fire neural networks, piecewise contractive maps and limit cycles ⋮ Stability of synchronous slowly oscillating periodic solutions for systems of delay differential equations with coupled nonlinearity ⋮ Synchronised firing patterns in a random network of adaptive exponential integrate-and-fire neuron model ⋮ Phase models and clustering in networks of oscillators with delayed coupling ⋮ Periodic orbits and chaos in fast-slow systems with Bogdanov-Takens type fold points ⋮ On the study of cellular nonlinear networks via amplitude and phase dynamics ⋮ The first, second and fourth Painlevé equations on weighted projective spaces ⋮ Learning-induced pattern classification in a chaotic neural network ⋮ Synchronization of weakly coupled canard oscillators ⋮ Analysis of chaotic oscillations induced in two coupled Wilson-Cowan models ⋮ Spatiotemporal control to eliminate cardiac alternans using isostable reduction ⋮ Nonlinear complexity of human biodynamics engine ⋮ Greater accuracy and broadened applicability of phase reduction using isostable coordinates ⋮ Stability of twisted states in the Kuramoto model on Cayley and random graphs ⋮ Total and partial amplitude death in networks of diffusively coupled oscillators ⋮ Towards Google matrix of brain ⋮ Two-cluster bifurcations in systems of globally pulse-coupled oscillators ⋮ Coupling-induced oscillations in two intrinsically quiescent populations ⋮ Dynamical systems on lattices with decaying interaction. I: A functional analysis framework ⋮ Non-stationary syllables in birdsong: an example ⋮ Analytic approximations of statistical quantities and response of noisy oscillators ⋮ Network dynamics: tools and examples ⋮ Types of bifurcations of FitzHugh-Nagumo maps ⋮ Collective dynamics and bifurcations in symmetric networks of phase oscillators. I ⋮ Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review ⋮ Extracellular potassium dynamics in the hyperexcitable state of the neuronal ictal activity ⋮ Nearest matrix with prescribed eigenvalues and its applications ⋮ Codimension-two bursting analysis in the delayed neural system with external stimulations ⋮ Dynamical regimes underlying epileptiform events: role of instabilities and bifurcations in brain activity ⋮ The robustness of phase-locking in neurons with dendro-dendritic electrical coupling ⋮ Synchronization of coupled limit cycles ⋮ Frustration induced transient chaos, fractal and riddled basins in coupled limit cycle oscillators ⋮ Intra- and intersegmental neural network architectures determining rhythmic motor activity in insect locomotion ⋮ Controlling the global behavior of coupled chaotic systems by means of energy regulation. ⋮ Phase description of nonlinear dissipative waves under space-time-dependent external forcing ⋮ Synchronization in complex networks of phase oscillators: a survey ⋮ Synchronization stability and firing transitions in two types of class I neuronal networks with short-term plasticity ⋮ Different types of bursting calcium oscillations in non-excitable cells ⋮ Bifurcation of discontinuous limit cycles of the Van der Pol equation ⋮ Self-synchronization of the integrate-and-fire pacemaker model with continuous couplings ⋮ Existence and robustness of phase-locking in coupled Kuramoto oscillators under mean-field feedback ⋮ Phase reduction and phase-based optimal control for biological systems: a tutorial ⋮ Entrainment ranges for chains of forced neural and phase oscillators ⋮ Spatially localized cluster solutions in inhibitory neural networks ⋮ Phase-amplitude descriptions of neural oscillator models ⋮ Optimal entrainment with smooth, pulse, and square signals in weakly forced nonlinear oscillators ⋮ Contraction of monotone phase-coupled oscillators ⋮ Feedforward networks: adaptation, feedback, and synchrony ⋮ Dynamics of a class of nonlinear discrete-time neural networks ⋮ Emerging dynamics in neuronal networks of diffusively coupled hard oscillators ⋮ A canonical model for gradient frequency neural networks ⋮ Reduction of a model of an excitable cell to a one-dimensional map ⋮ Type I vs. type II excitable systems with delayed coupling ⋮ The mechanisms for compression and reflection of cortical waves ⋮ The Kuramoto model on power law graphs: synchronization and contrast states ⋮ The roles of the Moran effect and dispersal in synchronizing oscillating populations ⋮ Vibrational resonance in neuron populations with hybrid synapses ⋮ Numerical solution of Volterra integral and integro-differential equations with rapidly vanishing convolution kernels ⋮ The almost sure stability of coupled system of stochastic delay differential equations on networks ⋮ Synchronization of oscillators coupled through an environment ⋮ Waves and patterns in ring lattices with delays ⋮ Duration of transient oscillations in ring networks of unidirectionally coupled neurons ⋮ Matrix perturbation analysis for weakly coupled oscillators ⋮ Symmetry and phase-locking in a ring of pulse-coupled oscillators with distributed delays ⋮ Travelling waves in chains of pulse-coupled integrate-and-fire oscillators with distributed delays ⋮ Cell-to-cell mathematical modeling of arrhythmia phenomena in the heart ⋮ Asymmetry of synchronisation tongue in persistent sodium plus potassium neuron model ⋮ The order-oscillation induced by negative feedback in the adaptive scheme ⋮ Mathematical framework for breathing Chimera states ⋮ Reliability of coupled oscillators ⋮ Bursting of Morris-Lecar neuronal model with current-feedback control ⋮ Global-stability problem for coupled systems of differential equations on networks ⋮ Awakened oscillations in coupled consumer-resource pairs ⋮ Fastest strategy to achieve given number of neuronal firing in theta model ⋮ Chaos and asymptotical stability in discrete-time recurrent neural networks with generalized input-output function ⋮ Phase description of oscillatory convection with a spatially translational mode
This page was built for publication: Weakly connected neural networks
