A Brief History of Excitable Map-Based Neurons and Neural Networks

Abstract

This review gives a short historical account of the excitable maps approach for modeling neurons and neuronal networks. Some early models, due to Pasemann (1993), Chialvo (1995) and Kinouchi and Tragtenberg (1996), are compared with more recent proposals by Rulkov (2002) and Izhikevich (2003). We also review map-based schemes for electrical and chemical synapses and some recent findings as critical avalanches in map-based neural networks. We conclude with suggestions for further work in this area like more efficient maps, compartmental modeling and close dynamical comparison with conductance-based models.

53 pages, 13 figures, submitted to Journal of Neuroscience Methods

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Cited by in corpus (17)

• Self-Organized Supercriticality and Oscillations in Networks of Stochastic Spiking Neurons
• Critical Avalanches and Subsampling in Map-based Neural Networks
• A modular architecture for transparent computation in Recurrent Neural Networks
• Observability and Synchronization of Neuron Models
• Synaptic Plasticity and Spike Synchronisation in Neuronal Networks
• Transient sequences in a hypernetwork generated by an adaptive network of spiking neurons
• Cardiac Reentry Modeled by Spatiotemporal Chaos in a Coupled Map Lattice
• An absorbing set for the Chialvo map
• Building a model of the brain: from detailed connectivity maps to network organization
• The Discrete Langevin Machine: Bridging the Gap Between Thermodynamic and Neuromorphic Systems
• A spiking photonic neural network of 40.000 neurons, trained with rank-order coding for leveraging sparsity
• Spontaneous organizations of diverse network structures in coupled logistic maps with a delayed connection change
• Optimal input reverberation and homeostatic self-organization towards the edge of synchronization
• Self Tuned Criticality: Controlling a neuron near its bifurcation point via temporal correlations
• Self-Organization of Diverse Directional Hierarchical Networks in Simple Coupled Maps with Connection Changes
• Devil's staircase inside shrimp-shaped regions reveals periodicity of plateau spikes and bursts
• Finite-time scaling on low-dimensional map bifurcations