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

By Gerasimos G. Rigatos

This e-book offers a whole examine on neural buildings showing nonlinear and stochastic dynamics, elaborating on neural dynamics via introducing complex types of neural networks. It overviews the most findings within the modelling of neural dynamics by way of electric circuits and examines their balance homes with using dynamical platforms thought.

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

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Additional resources for Advanced Models of Neural Networks: Nonlinear Dynamics and Stochasticity in Biological Neurons

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I / D Ä C p Ä 2 C A2 I , where Ä D A2 ag=2. 102) 2. Calcium-activated nonspecific cation current This case is concerned with the inwards calcium current ICAN . c/ is a monotonous function of the concentration of Ca2C . 105) The rate of the voltage spikes in a membrane characterized by calcium-activated nonspecific cation (CAN) current increases each time calcium stimuli arrives. 9 Conclusions In this chapter it has been shown that the functioning of the cells membrane can be represented as an electric circuit.

0; 0/. 3 Stability Analysis of the Morris–Lecar Nonlinear Model Local stability of the Morris–Lecar model can be studied round the associated equilibria. Local linearization can be performed round equilibria. Using the set of differential equations that describe the Morris–Lecar neuron that was given in Eq. x x0 / C one obtains the system’s local linear dynamics. V /. The fixed points of this model are computed from the condition xP 1 D 0 and xP 2 D 0. VR / ! 49) The eigenvalues of matrix M define stability round fixed points (stable or unstable fixed point).

3 Calcium Channels Ca2C The equation of the current of the associated channel is given by the constant field equation, given in Eq. 86). Calcium channels are distinguished in two large categories: 1. V /. 2. V /. T -currents exhibit bursts and subthreshold oscillations. 1 C exp. V C 48/=4/ C exp. V C 407=50// The response of this model depends on the activation variable m and on the deactivation variable h. 4 Voltage-Gated Potassium Channels KC These are ion channels which open or close depending on the value of the membrane’s potential V .

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