Poincaré return maps in neural dynamics: three examples

DOI10.1007/978-3-030-60107-2_3zbMath1471.37078arXiv2007.05595OpenAlexW3161210613MaRDI QIDQ2050465

Marina L. Kolomiets, Andrej L. Shil'nikov

Publication date: 31 August 2021

Full work available at URL: https://arxiv.org/abs/2007.05595

zbMATH Keywords

networksneural modelneurodynamicsPoincaré return maps

Mathematics Subject Classification ID

Dynamical systems in biology (37N25) Neural networks for/in biological studies, artificial life and related topics (92B20)

Related Items (1)

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Cites Work

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• Burst-duration mechanism of in-phase bursting in inhibitory networks
• Chaos in a three-variable model of an excitable cell
• Dynamical systems V. Bifurcation theory and catastrophe theory. Transl. from the Russian by N. D. Kazarinoff
• A mathematical criterion based on phase response curves for stability in a ring of coupled oscillators
• On bifurcations of the Lorenz attractor in the Shimizu-Morioka model
• Tracking invariant manifolds with differential forms in singularly perturbed systems
• Topological and phenomenological classification of bursting oscillations
• Mechanisms for oscillation and frequency control in reciprocally inhibitory model neural networks
• Complete dynamical analysis of a neuron model
• Voltage interval mappings for activity transitions in neuron models for elliptic bursters
• Subthreshold oscillations in a map-based neuron model
• Qualitative and quantitative stability analysis of penta-rhythmic circuits
• Return Map Characterizations for a Model of Bursting with Two Slow Variables
• ORIGIN OF CHAOS IN A TWO-DIMENSIONAL MAP MODELING SPIKING-BURSTING NEURAL ACTIVITY

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