Stephen Coombes is a Professor of Applied Mathematics at the University of Nottingham, UK.  His research interest is in the use of nonlinear dynamics to understand aspects of the human central nervous system. He has co-edited two books and authored over 120 peer-reviewed journal articles.  He has supervised 22 PhD students and 8 postdoctoral fellows.Together with colleagues in Mathematics and Neuroscience he is actively pursuing research projects ranging from single cell dynamics to neuronal circuits to whole-brain dynamics with applications in psychology, neuroimaging, medicine, and psychiatry. Kyle Wedgwood is a Lecturer in Mathematics in the Living Systems Institute at the University of Exeter, UK. He applies techniques from dynamical systems theory to understand how electrically excitable cells produce coherent rhythms in networks and has authored 22 peer-reviewed journal articles. He currently supervises 4 PhD students and 2 postdoctoral fellows. In his current research, he is exploring how mathematics can be embedded in neuroscience experiments.

• Overview.- Single neuron models-. Phenomenological models and their analysis.- Axons, dendrites, and synapses.- Response properties of single neurons.- Weakly coupled oscillator networks.- Strongly coupled spiking networks.- Population models.- Firing rate tissue models.- Stochastic calculus.- Model Details.- References.

Stephen Coombes is a Professor of Applied Mathematics at the University of Nottingham, UK.  His research interest is in the use of nonlinear dynamics to understand aspects of the human central nervous system. He has co-edited two books and authored over 120 peer-reviewed journal articles.  He has supervised 22 PhD students and 8 postdoctoral fellows.Together with colleagues in Mathematics and Neuroscience he is actively pursuing research projects ranging from single cell dynamics to neuronal circuits to whole-brain dynamics with applications in psychology, neuroimaging, medicine, and psychiatry. Kyle Wedgwood is a Lecturer in Mathematics in the Living Systems Institute at the University of Exeter, UK. He applies techniques from dynamical systems theory to understand how electrically excitable cells produce coherent rhythms in networks and has authored 22 peer-reviewed journal articles. He currently supervises 4 PhD students and 2 postdoctoral fellows. In his current research, he is exploring how mathematics can be embedded in neuroscience experiments.

• Overview.- Single neuron models-. Phenomenological models and their analysis.- Axons, dendrites, and synapses.- Response properties of single neurons.- Weakly coupled oscillator networks.- Strongly coupled spiking networks.- Population models.- Firing rate tissue models.- Stochastic calculus.- Model Details.- References.