Download Advanced Models of Neural Networks: Nonlinear Dynamics and by Gerasimos G. Rigatos PDF

By Gerasimos G. Rigatos

ISBN-10: 3662437635

ISBN-13: 9783662437636

This ebook offers a whole examine on neural constructions displaying nonlinear and stochastic dynamics, elaborating on neural dynamics via introducing complicated versions of neural networks. It overviews the most findings within the modelling of neural dynamics when it comes to electric circuits and examines their balance houses with using dynamical platforms idea.

It is appropriate for researchers and postgraduate scholars engaged with neural networks and dynamical structures theory.

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Extra info for Advanced Models of Neural Networks: Nonlinear Dynamics and Stochasticity in Biological Neurons

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75) q d where D 4rrML is the space constant and D rM cM is the time constant. x/ D Ae . 3 The Infinite Length Cable The relation given in Eq. 75) is modified in case of an infinite length cable. x/. x; t / has units A=cm2 . k/ C . x; t / D q 1 2t 4 e t e x 2 =. e. x; t / D rp M I0 4 t e tx 2 4 2 Á e. e. 1 Types of Ion Channels In the set of equations that constitute the Hodgkin–Huxley model one can distinguish the KC and NaC ion channels, whereas in the Morris–Lecar model one can distinguish the CaC model.

Sodium channels of the Hodgkin–Huxley model have both activation and inactivation. Channel KC of the Hodgkin–Huxley model, and channels Ca2C and KC of the Morris–Lecar model do not exhibit inactivation. 86) zVF RT where the units of gmax are Siemens/cm2 and cf e means constant field equation. In the equation about the channel’s current Eq. V VT /=K / V amp =cosh. 89) A key parameter for the appearance and density of voltage pulses is the leak potential EL . According to the value of this parameter, at points of the membrane, the variation of the voltage V in time may take the form of spikes or bursts.

75) q d where D 4rrML is the space constant and D rM cM is the time constant. x/ D Ae . 3 The Infinite Length Cable The relation given in Eq. 75) is modified in case of an infinite length cable. x/. x; t / has units A=cm2 . k/ C . x; t / D q 1 2t 4 e t e x 2 =. e. x; t / D rp M I0 4 t e tx 2 4 2 Á e. e. 1 Types of Ion Channels In the set of equations that constitute the Hodgkin–Huxley model one can distinguish the KC and NaC ion channels, whereas in the Morris–Lecar model one can distinguish the CaC model.

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