Advanced Models of Neural Networks: Nonlinear Dynamics and - download pdf or read online
By Gerasimos G. Rigatos
This booklet offers a whole research on neural buildings showing nonlinear and stochastic dynamics, elaborating on neural dynamics by means of 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 houses with using dynamical structures conception.
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
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. 51) The associated phase diagram is designed for different initial conditions and is given in Fig. 14. 4 Phase Diagrams and Equilibria of Neuronal Models Fig. 8 −1 −8 −6 −4 −2 0 x Fig.
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.
5) Example 2. Tunnel diode circuit (Fig. 2). 9) 30 2 Systems Theory for the Analysis of Biological Neuron Dynamics The following state variables are defined x1 D VC and x2 D iL . From Eq. 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.
Advanced Models of Neural Networks: Nonlinear Dynamics and Stochasticity in Biological Neurons by Gerasimos G. Rigatos