Synchronization and stable phase-locking in a network of neurons with memory

Wu, Jianhong; Faria, Teresa; Huang, Yihong

doi:10.1016/s0895-7177(99)00120-x

Cited by 87 publications

(50 citation statements)

References 16 publications

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“…The delay can cancel or amplify multiple spikes thus leading to the neural information being selectively processed. The theoretical study of the dynamics of simple units organized into networks with delayed couplings revealed a rich variety of possible scenarios of transition to a global oscillatory behavior induced by the delay (see, e.g., Bungay and Campbell 2007;Campbell et al 2005;Guo 2005; Guo and Huang 2003;Guo 2007;Huang and Wu 2003;Song et al 2005;Wu et al 1999;Wu 1998;Yuan and Campbell 2004;Yuan 2007;Wei et al 2002;Wei and Velarde 2004 and references therein). The emerging oscillations can exhibit different spatio-temporal patterns sensitive to the delay.…”

Section: Introductionmentioning

confidence: 99%

Stability switches, oscillatory multistability, and spatio-temporal patterns of nonlinear oscillations in recurrently delay coupled neural networks

2009

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A model of time-delay recurrently coupled spatially segregated neural assemblies is here proposed. We show that it operates like some of the hierarchical architectures of the brain. Each assembly is a neural network with no delay in the local couplings between the units. The delay appears in the long range feedforward and feedback inter-assemblies communications. Bifurcation analysis of a simple four-units system in the autonomous case shows the richness of the dynamical behaviors in a biophysically plausible parameter region. We find oscillatory multistability, hysteresis, and stability switches of the rest state provoked by the time delay. Then we investigate the spatio-temporal patterns of bifurcating periodic solutions by using the symmetric local Hopf bifurcation theory of delay differential equations and derive the equation describing the flow on the center manifold that enables us determining the direction of Hopf bifurcations and stability of the bifurcating periodic orbits. We also discuss computational properties of the system due to the delay when an external drive of the network mimicks external sensory input.

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Section: Introductionmentioning

confidence: 99%

Stability switches, oscillatory multistability, and spatio-temporal patterns of nonlinear oscillations in recurrently delay coupled neural networks

2009

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“…The above argument applies to systems with arbitrary even n. So synchronous periodic solutions of network (1) arising from the slowly oscillatory periodic solutions of (2) are always unstable for the network (1) with either large n or arbitrary even n. However, these synchronous periodic solutions can be stable under possible perturbations if n is odd and small. Examples of this type will be given in the case study of Wu, Faria and Huang [15].…”

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confidence: 99%

Desynchronization of large scale delayed neural networks

Chen

Huang

2000

Proc. Amer. Math. Soc.

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Abstract. We consider a ring of identical neurons with delayed nearest neighborhood inhibitory interaction. Under general conditions, such a network has a slowly oscillatory synchronous periodic solution which is completely characterized by a scalar delay differential equation with negative feedback. Despite the fact that the slowly oscillatory periodic solution of the scalar equation is stable, we show that the associated synchronous solution is unstable if the size of the network is large.

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“…We would like to mention that there are several articles on the bifurcations for neural network models with delays, and we refer the reader to [20][21][22][23][24][25][26][27] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Hopf bifurcation analysis in synaptically coupled HR neurons with two time delays

2010

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This paper presents an investigation of stability and Hopf bifurcation of a synaptically coupled nonidentical HR model with two time delays. By regarding the half of the sum of two delays as a parameter, we first consider the existence of local Hopf bifurcations, and then derive explicit formulas for determining the direction of the Hopf bifurcations and the stability of bifurcating periodic solutions, using the normal form method and center manifold theory. Finally, numerical simulations are carried out for supporting theoretical analysis results.

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Synchronization and stable phase-locking in a network of neurons with memory

Cited by 87 publications

References 16 publications

Stability switches, oscillatory multistability, and spatio-temporal patterns of nonlinear oscillations in recurrently delay coupled neural networks

Stability switches, oscillatory multistability, and spatio-temporal patterns of nonlinear oscillations in recurrently delay coupled neural networks

Desynchronization of large scale delayed neural networks

Hopf bifurcation analysis in synaptically coupled HR neurons with two time delays

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