LEADER 04072nam 22006015 450 001 9910725093103321 005 20251113210439.0 010 $a9783031219160$b(electronic bk.) 010 $z9783031219153 024 7 $a10.1007/978-3-031-21916-0 035 $a(MiAaPQ)EBC7247415 035 $a(Au-PeEL)EBL7247415 035 $a(OCoLC)1378933490 035 $a(DE-He213)978-3-031-21916-0 035 $a(PPN)270612807 035 $a(CKB)26624134300041 035 $a(EXLCZ)9926624134300041 100 $a20230509d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNeurodynamics $eAn Applied Mathematics Perspective /$fby Stephen Coombes, Kyle C. A. Wedgwood 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (513 pages) 225 1 $aTexts in Applied Mathematics,$x2196-9949 ;$v75 311 08$aPrint version: Coombes, Stephen Neurodynamics Cham : Springer International Publishing AG,c2023 9783031219153 320 $aIncludes bibliographical references and index. 327 $aOverview -- 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. 330 $aThis book is about the dynamics of neural systems and should be suitable for those with a background in mathematics, physics, or engineering who want to see how their knowledge and skill sets can be applied in a neurobiological context. No prior knowledge of neuroscience is assumed, nor is advanced understanding of all aspects of applied mathematics! Rather, models and methods are introduced in the context of a typical neural phenomenon and a narrative developed that will allow the reader to test their understanding by tackling a set of mathematical problems at the end of each chapter. The emphasis is on mathematical- as opposed to computational-neuroscience, though stresses calculation above theorem and proof. The book presents necessary mathematical material in a digestible and compact form when required for specific topics. The book has nine chapters, progressing from the cell to the tissue, and an extensive set of references. It includes Markov chain models for ions, differential equations for single neuron models, idealised phenomenological models, phase oscillator networks, spiking networks, and integro-differential equations for large scale brain activity, with delays and stochasticity thrown in for good measure. One common methodological element that arises throughout the book is the use of techniques from nonsmooth dynamical systems to form tractable models and make explicit progress in calculating solutions for rhythmic neural behaviour, synchrony, waves, patterns, and their stability. This book was written for those with an interest in applied mathematics seeking to expand their horizons to cover the dynamics of neural systems. It is suitable for a Masters level course or for postgraduate researchers starting in the field of mathematical neuroscience. 410 0$aTexts in Applied Mathematics,$x2196-9949 ;$v75 606 $aBiomathematics 606 $aDynamics 606 $aNonlinear theories 606 $aMathematical and Computational Biology 606 $aApplied Dynamical Systems 615 0$aBiomathematics. 615 0$aDynamics. 615 0$aNonlinear theories. 615 14$aMathematical and Computational Biology. 615 24$aApplied Dynamical Systems. 676 $a612.8 676 $a612.82330151 700 $aCoombes$b Stephen$01195880 702 $aWedgwood$b Kyle C. A. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910725093103321 996 $aNeurodynamics$93366968 997 $aUNINA