Journal of Computational Neuroscience
, Volume 26, Issue 3, pp 425443
First online:
Synchronization dynamics of two coupled neural oscillators receiving shared and unshared noisy stimuli
 Cheng LyAffiliated withDepartment of Mathematics, University of Pittsburgh Email author
 , G. Bard ErmentroutAffiliated withUniversity Professor of Computational Biology, Professor, Department of Mathematics, University of Pittsburgh
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The response of neurons to external stimuli greatly depends on the intrinsic dynamics of the network. Here, the intrinsic dynamics are modeled as coupling and the external input is modeled as shared and unshared noise. We assume the neurons are repetitively firing action potentials (i.e., neural oscillators), are weakly and identically coupled, and the external noise is weak. Shared noise can induce bistability between the synchronous and antiphase states even though the antiphase state is the only stable state in the absence of noise. We study the FokkerPlanck equation of the system and perform an asymptotic reduction ρ _{0}. The ρ _{0} solution is more computationally efficient than both the Monte Carlo simulations and the 2D FokkerPlanck solver, and agrees remarkably well with the full system with weak noise and weak coupling. With moderate noise and coupling, ρ _{0} is still qualitatively correct despite the small noise and coupling assumption in the asymptotic reduction. Our phase model accurately predicts the behavior of a realistic synaptically coupled MorrisLecar system.
Keywords
Neural oscillators Shared noise Weak coupling Weak noise Bistability Title
 Synchronization dynamics of two coupled neural oscillators receiving shared and unshared noisy stimuli
 Journal

Journal of Computational Neuroscience
Volume 26, Issue 3 , pp 425443
 Cover Date
 200906
 DOI
 10.1007/s1082700801208
 Print ISSN
 09295313
 Online ISSN
 15736873
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Neural oscillators
 Shared noise
 Weak coupling
 Weak noise
 Bistability
 Industry Sectors
 Authors

 Cheng Ly ^{(1)}
 G. Bard Ermentrout ^{(2)}
 Author Affiliations

 1. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA
 2. University Professor of Computational Biology, Professor, Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA