## Mathematical Foundations of NeuroscienceArising from several courses taught by the authors, this book provides a needed overview illustrating how dynamical systems and computational analysis have been used in understanding the types of models that come out of neuroscience. |

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### Contents

Chapter 1 The HodgkinHuxley Equations | 1 |

Chapter 2 Dendrites | 29 |

Chapter 3 Dynamics | 49 |

Chapter 4 Th e Variety of Channels | 77 |

Chapter 5 Bursting Oscillations | 102 |

Chapter 6 Propagating Action Potentials | 129 |

Chapter 7 Synaptic Channels | 157 |

Chapter 8 Neural Oscillators Weak Coupling | 171 |

Chapter 9 Neuronal Networks FastSlow Analysis | 241 |

Chapter 10 Noise | 285 |

Chapter 11 Firing Rate Models | 331 |

Chapter 12 Spatially Distributed Networks | 368 |

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### Other editions - View all

Mathematical Foundations of Neuroscience G. Bard Ermentrout,David H. Terman No preview available - 2012 |

### Common terms and phrases

action potential active phase adjoint analysis antiphase antiphase solution applied current assume axon behavior bifurcation diagram bistability boundary conditions cable calcium cells fire channels compute consider constant corresponding coupling cubic defined dendritic depends depolarizing derive differential equation dV dt dynamics eigenvalues example excitatory Exercise fast subsystem Figure frequency function homoclinic orbit Hopf bifurcation hyperpolarizing Iapp inhibition inhibitory input integral integrate-and-fire model ions jump left branch limit cycle linear mathematical membrane potential Morris–Lecar model neural neural oscillators neurons noise nonlinear Note nullcline ŒCa oscillations parameters periodic orbits periodic solution perturbation phase plane postsynaptic potassium presynaptic reset resting reversal potential right branch saddle–node satisfies scalar shown in Fig shows silent phase simulation singular slow variables spike Springer Science+Business Media stable fixed point stable limit cycle stable manifold steady-state stimulus Suppose synapses synchronous threshold timescale trajectory unstable V-nullcline velocity voltage zero