Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting

By Eugene M. Izhikevich. 2006

3,325 citations recorded by the source corpus.

Subfields: Cellular and Molecular Neuroscience, Cognitive Neuroscience, Plant Science

View Paper: https://www.semanticscholar.org/paper/c90778b804faf8d3ad7cd6164865809394fa58e5

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In Cellular and Molecular Neuroscience

In Cognitive Neuroscience

In Plant Science

Citations in the corpus

Revealing networks from dynamics: an introduction (2014, methodology): “Moreover, widely used model systems for networks of neurons, such as leaky integrate-andfire and quadratic integrate-and-fire neurons [50] or networks of coupled chaotic systems such as Rössler or Lorenz systems [51, 52] exhibit all or at least most parameters occurring linearly or affinely.”
Synchronization in complex networks of phase oscillators: A survey (2014, methodology): “Our presentation is informal, we schematically follow the approaches developed in the computational neuroscience community, andwe refer to the textbooks (Hoppensteadt& Izhikevich, 1997; Izhikevich, 2007), the tutorials (Izhikevich & Kuramoto, 2006; Mauroy et al.”
Towards Physics-informed Deep Learning for Turbulent Flow Prediction (2019, background): “Methods in dynamical system literature from physics [11]”
Broadcast and Weight: An Integrated Network For Scalable Photonic Spike Processing (2014, background): “This distributed, asynchronous model processes information using both space and time [4]–[6], and is amenable to distributed, unsupervised adaptation [7], [8].”
The Dynamic Brain: From Spiking Neurons to Neural Masses and Cortical Fields (2008, methodology): “Each neuron is modeled as a planar reduction of the Hodgkin-Huxley model [109,110], namely,”
Mathematical framework for large-scale brain network modeling in The Virtual Brain (2015, neutral): “The manipulation of the latter nullcline's parameters allows for the generation of a wide range of dynamic behaviors (Izhikevich, 2007).”
Codimension-two bursting analysis in the delayed neural system with external stimulations (2012, background): “7, which can be referred from [7, 23].”
Network Reconstruction From High-Dimensional Ordinary Differential Equations (2016, background): “Ordinary differential equations (ODEs) have been widely used to model dynamical systems in many ﬁelds, including chemical engineering (Biegler et al., 1986), genomics (Chou and Voit, 2009), neuroscience (Izhikevich, 2007), and infectious diseases (Wu, 2005).”
Spatiotemporal dynamics of continuum neural fields (2012, background): “A common bifurcation scenario in conductance-based models of cortical neurons is a saddle node on an invariant circle [31, 36], so that close to the bifurcation point, see figure 2, we have”
A Scalable Multicore Architecture With Heterogeneous Memory Structures for Dynamic Neuromorphic Asynchronous Processors (DYNAPs) (2017, background): “tra variables in the dynamic equation of the neuron that endow it with a wide variety of dynamical behaviors [27], [28].”
Computational models of schizophrenia and dopamine modulation in the prefrontal cortex (2008, background): “…of frequencies in patients with schizophrenia ( broadband phase synchrony ) raises the possibility that there are intrinsic deficits in the brain circuitry that supports oscillations in several frequency bands (perhaps indicating increased noise in spiking neurons, as outlined above) 102–106 .”
Stochastic theory of nonequilibrium steady states and its applications. Part I (2012, background): “Even though this simplemodel often is not sufficient in describing the dynamics of a real neuron [159,160], it is expected to provide great insights for dynamics of neural networks where emergent properties are usually insensitive to the details of underlying single neurons.”