Role of Delays in Shaping Spatiotemporal Dynamics of Neuronal Activity in Large Networks

Roxin, Alex; Brunel, Nadège; Hansel, David

doi:10.1103/physrevlett.94.238103

Cited by 275 publications

(267 citation statements)

References 21 publications

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“…These authors modelled heterogeneity by putting a direct connection from one part of the domain to another and studied the effect of varying the length of this connection. Roxin et al (2005) recently studied a generalisation of a neural field model first presented by Hansel & Sompolinsky (1998) in which there is a fixed delay in the nonlinear term, as opposed to the space-dependent delays that we have. This delay is meant to mimic those due to synaptic and dendritic processing.…”

Section: Discussionmentioning

confidence: 99%

The importance of different timings of excitatory and inhibitory pathways in neural field models

Laing

Coombes

2006

Network: Computation in Neural Systems

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In this paper, we consider a neural field model comprised of two distinct populations of neurons, excitatory and inhibitory, for which both the velocities of action potential propagation and the time courses of synaptic processing are different. Using recently-developed techniques, we construct the Evans function characterising the stability of both stationary and travelling wave solutions, under the assumption that the firing rate function is the Heaviside step. We find that these differences in timing for the two populations can cause instabilities of these solutions, leading to, for example, stationary breathers. We also analyse "anti-pulses", a novel type of pattern for which all but a small interval of the domain (in moving coordinates) is active. These results extend previous work on neural fields with space-dependent delays, and demonstrate the importance of considering the effects of the different time-courses of excitatory and inhibitory neural activity.

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Section: Discussionmentioning

confidence: 99%

The importance of different timings of excitatory and inhibitory pathways in neural field models

Laing

Coombes

2006

Network: Computation in Neural Systems

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“…As a consequence, if one wants to uncover the dynamics beyond numerical investigations, one is often restricted to mean field theoretical arguments or focuses on globally connected networks or on networks of simple local topology. [2][3][4][5][6][7][8][9][10][11] Here we follow the simple and very useful approach of Mirollo and Strogatz 12 to represent the state of a onedimensional ͑neural͒ oscillator not by its membrane potential, but by a phase that encodes the time to the next spike in the absence of any interactions. In the limit of infinitely fast processing of incoming signals ͑post-synaptic currents͒, the nonlinear interactions can then be treated analytically in an exact manner.…”

Section: Introductionmentioning

confidence: 99%

Speed of synchronization in complex networks of neural oscillators: Analytic results based on Random Matrix Theory

Timme

Geisel

Wolf

2006

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We analyze the dynamics of networks of spiking neural oscillators. First, we present an exact linear stability theory of the synchronous state for networks of arbitrary connectivity. For general neuron rise functions, stability is determined by multiple operators, for which standard analysis is not suitable. We describe a general nonstandard solution to the multioperator problem. Subsequently, we derive a class of neuronal rise functions for which all stability operators become degenerate and standard eigenvalue analysis becomes a suitable tool. Interestingly, this class is found to consist of networks of leaky integrate-and-fire neurons. For random networks of inhibitory integrate-and-fire neurons, we then develop an analytical approach, based on the theory of random matrices, to precisely determine the eigenvalue distributions of the stability operators. This yields the asymptotic relaxation time for perturbations to the synchronous state which provides the characteristic time scale on which neurons can coordinate their activity in such networks. For networks with finite in-degree, i.e., finite number of presynaptic inputs per neuron, we find a speed limit to coordinating spiking activity. Even with arbitrarily strong interaction strengths neurons cannot synchronize faster than at a certain maximal speed determined by the typical in-degree. © 2006 American Institute of Physics. ͓DOI: 10.1063/1.2150775͔The individual units of many physical systems, from the planets of our solar system to the atoms in a solid, typically interact continuously in time and without significant delay. Thus at every instant of time such a unit is influenced by the current state of its interaction partners. Moreover, particles of many-body systems are often considered to have very simple lattice topology (as in a crystal) or no prescribed topology at all (as in an ideal gas). Many important biological systems are drastically different: their units are interacting by sending and receiving pulses at discrete instances of time. Furthermore, biological systems often exhibit significant delays in the couplings and very complicated topologies of their interaction networks. Examples of such systems include neurons, which interact by stereotyped electrical pulses called action potentials or spikes; crickets, which chirp to communicate acoustically; populations of fireflies that interact by short light pulses. The combination of pulsecoupling, delays, and complicated network topology formally makes the dynamical system to be investigated a high dimensional, heterogeneous nonlinear hybrid system with delays. Here we present an exact analysis of aspects of the dynamics of such networks in the case of simple one-dimensional nonlinear interacting units. These systems are simple models for the collective dynamics of recurrent networks of spiking neurons. After briefly presenting stability results for the synchronous state, we show how to use the theory of random matrices to analytically predict the eigenvalue distribution of stability matrices and t...

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“…In this paper, the CPG is treated as the proprioception from the musculoskeletal system and is fed back to the basal ganglia. The researchers have already revealed that time delays can gradually affect the spatio-temporal dynamics in networks of coupled neurons (Roxin et al 2005). Therefore, when the CPG signal is sent to the basal ganglia, the time delay should be considered.…”

Section: Introductionmentioning

confidence: 99%

Effects on hypothalamus when CPG is fed back to basal ganglia based on KIV model

Tian

et al. 2014

Cogn Neurodyn

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The KIV model approximates the operation of the basic vertebrate forebrain together with the basal ganglia and motor systems. In KIV model, the hypothalamus and the basal ganglia which are two important parts in the midline forebrain are closely associated with the locomotion. The CPG model with time delay is established in this paper and the stability of this CPG model is discussed. The CPG output is treated as the proprioception and fed back to the basal ganglia. We focus on the effects on the hypothalamus and the basal ganglia when the time delay parameter a d , the CPG amplitude parameter e and the CPG frequency parameter T r are changed. Through analysis, we find that there exists optimum value of the parameters a d or T r which can make the synchronization of the hypothalamus optimum when the CPG is added into the basal ganglia. The results could have important implications for biological processes which are about interaction between the neural network and the CPG.

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Role of Delays in Shaping Spatiotemporal Dynamics of Neuronal Activity in Large Networks

Cited by 275 publications

References 21 publications

The importance of different timings of excitatory and inhibitory pathways in neural field models

The importance of different timings of excitatory and inhibitory pathways in neural field models

Speed of synchronization in complex networks of neural oscillators: Analytic results based on Random Matrix Theory

Effects on hypothalamus when CPG is fed back to basal ganglia based on KIV model

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