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 Nicks2016-01-06T00:00:00ZPath 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. Buice2015-03-24T00:00:00ZUnderstanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a reviewhttps://mathematical-neuroscience.springeropen.com/articles/10.1186/s13408-020-00086-9Many biological and neural systems can be seen as networks of interacting periodic processes. Importantly, their functionality, i.e., whether these networks can perform their function or not, depends on the em...ReviewWed, 27 May 2020 00:00:00 GMThttps://mathematical-neuroscience.springeropen.com/articles/10.1186/s13408-020-00086-9Christian Bick, Marc Goodfellow, Carlo R. Laing and Erik A. Martens2020-05-27T00:00:00ZA 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 Kramer2012-02-21T00:00:00Z