By Gerasimos G. Rigatos
This ebook presents an entire examine on neural buildings displaying nonlinear and stochastic dynamics, elaborating on neural dynamics through introducing complicated types of neural networks. It overviews the most findings within the modelling of neural dynamics by way of electric circuits and examines their balance houses with using dynamical platforms conception.
It is appropriate for researchers and postgraduate scholars engaged with neural networks and dynamical platforms theory.
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Extra info for Advanced Models of Neural Networks: Nonlinear Dynamics and Stochasticity in Biological Neurons
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. However, there may be more ion channels across the neuron’s membrane which are described as follows [16, 60, 65].
X/ @V . 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.
12. Case 3: Matrix A has non-zero eigenvalues which are equal to each other. The associated phase diagram is given in Fig. 13. 40 2 Systems Theory for the Analysis of Biological Neuron Dynamics Fig. 9 Phase diagram of state variables x1 , x2 of a second order linear autonomous system with real eigenvalues 1 > 2 > 0 3 2 x2 1 0 −1 −2 −3 −30 −20 −10 0 x 10 20 30 1 Fig. 2 Multiple Equilibria for Nonlinear Dynamical Systems A nonlinear system can have multiple equilibria as shown in the following example.
Advanced Models of Neural Networks: Nonlinear Dynamics and Stochasticity in Biological Neurons by Gerasimos G. Rigatos