By Gerasimos G. Rigatos
This booklet presents a whole learn on neural constructions displaying nonlinear and stochastic dynamics, elaborating on neural dynamics by way of introducing complicated types of neural networks. It overviews the most findings within the modelling of neural dynamics when it comes to electric circuits and examines their balance homes with using dynamical platforms concept.
It is acceptable for researchers and postgraduate scholars engaged with neural networks and dynamical structures theory.
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Additional info for Advanced Models of Neural Networks: Nonlinear Dynamics and Stochasticity in Biological Neurons
11) where u D E. Additionally, from Eq. 12) By replacing Eqs. 13) From Eqs. 17) Example 3. Spring-mass system (Fig. 3). 1 Characteristics of the Dynamics of Nonlinear Systems 31 Fig. x1 ; x2 /. x1 ; x2 / have a constant slope. x/ D c is drawn in the x1 x2 plane and along this curve one also draws small linear segments of length c. x/ D c is known as isocline. x1 ; x2 /. Example 1. 30) For different values of c one has the following isoclines diagram depicted in Fig. 4. 2 Computation of Isoclines 33 Fig.
V@x D 0. x; t /, in different parts of the dendrites (Fig. 11). For each smaller part in the dendrite that is characterized by spatially uniform potential, the major parameters are: the cylinder’s radius ˛i , the length Li , the membrane’s potential Vi , the capacitance (normalized per unit of surface) ci , and the resistance of the membrane (normalized per unit of surface) rLi . It is assumed that in each compartment there is an electrode to which external current Ielectrode is applied. 7 Modelling Dendrites in Terms of Electrical Circuits 17 Fig.
Some terminology associated with fixed points is as follows. A fixed point for the system of Eq. 50) is called hyperbolic if none of the eigenvalues of matrix A has zero real part. A hyperbolic fixed point is called a saddle if some of the eigenvalues of matrix A have real parts greater than zero and the rest of the eigenvalues have real parts less than zero. If all of the eigenvalues have negative real parts, then the hyperbolic fixed point is called a stable node or sink. If all of the eigenvalues have positive real parts, then the hyperbolic fixed point is called an unstable node or source.
Advanced Models of Neural Networks: Nonlinear Dynamics and Stochasticity in Biological Neurons by Gerasimos G. Rigatos