Most Accessed Articles: The Journal of Mathematical Neurosciencehttps://mathematical-neuroscience.springeropen.comMost Accessed Articles: The Journal of Mathematical NeuroscienceMean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neuronshttps://mathematical-neuroscience.springeropen.com/articles/10.1186/2190-8567-2-10We derive the mean-field equations arising as the limit of a network of interacting spiking neurons, as the number of neurons goes to infinity. The neurons belong to a fixed number of populations and are repre...ResearchThu, 31 May 2012 00:00:00 GMThttps://mathematical-neuroscience.springeropen.com/articles/10.1186/2190-8567-2-10Javier Baladron, Diego Fasoli, Olivier Faugeras and Jonathan Touboul2012-05-31T00:00:00ZMathematical Frameworks for Oscillatory Network Dynamics in Neurosciencehttps://mathematical-neuroscience.springeropen.com/articles/10.1186/s13408-015-0033-6The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to s...ReviewWed, 06 Jan 2016 00:00:00 GMThttps://mathematical-neuroscience.springeropen.com/articles/10.1186/s13408-015-0033-6Peter Ashwin, Stephen Coombes and Rachel Nicks2016-01-06T00:00:00ZA showcase of torus canards in neuronal burstershttps://mathematical-neuroscience.springeropen.com/articles/10.1186/2190-8567-2-3Rapid action potential generation - spiking - and alternating intervals of spiking and quiescence - bursting - are two dynamic patterns commonly observed in neuronal activity. In computational models of neuron...ResearchTue, 21 Feb 2012 00:00:00 GMThttps://mathematical-neuroscience.springeropen.com/articles/10.1186/2190-8567-2-3John Burke, Mathieu Desroches, Anna M Barry, Tasso J Kaper and Mark A Kramer2012-02-21T00:00:00ZParameter-sweeping techniques for temporal dynamics of neuronal systems: case study of Hindmarsh-Rose modelhttps://mathematical-neuroscience.springeropen.com/articles/10.1186/2190-8567-1-6Development of effective and plausible numerical tools is an imperative task for thorough studies of nonlinear dynamics in life science applications.ResearchMon, 11 Jul 2011 00:00:00 GMThttps://mathematical-neuroscience.springeropen.com/articles/10.1186/2190-8567-1-6Roberto Barrio and Andrey Shilnikov2011-07-11T00:00:00ZPath Integral Methods for Stochastic Differential Equationshttps://mathematical-neuroscience.springeropen.com/articles/10.1186/s13408-015-0018-5Stochastic differential equations (SDEs) have multiple applications in mathematical neuroscience and are notoriously difficult. Here, we give a self-contained pedagogical review of perturbative field theoretic...ResearchTue, 24 Mar 2015 00:00:00 GMThttps://mathematical-neuroscience.springeropen.com/articles/10.1186/s13408-015-0018-5Carson C. Chow and Michael A. Buice2015-03-24T00:00:00Z