By Gerasimos G. Rigatos
This publication presents an entire examine on neural buildings showing nonlinear and stochastic dynamics, elaborating on neural dynamics via 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 houses with using dynamical platforms concept.
It is appropriate 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
Additional models of reduced dimensionality that describe voltage variations along the neurons membrane have been introduced. These were the FitzHugh–Nagumo model and the Morris–Lecar model. It has been also demonstrated that cable’s equation is also shown to be suitable for describing voltage variations along dendrites. Finally, the various types of ionic channels and ion currents across the neurons membrane have been analyzed. Chapter 2 Systems Theory for the Analysis of Biological Neuron Dynamics Abstract The chapter analyzes the basics of systems theory which can be used in the modelling of biological neurons dynamics.
41) q M and M D cM rM . 0/. The solution of the partial differential equation given in Eq. x; t /. e. when @V@tM D 0, the partial differential equation becomes an ordinary differential equation of the form 2 d 2 Vss dx2 From Eq. 1. x/ D Time constant rL I0 ˛2 e affects the variation of voltage. 44) 12 1 Modelling Biological Neurons in Terms of Electrical Circuits Fig. x; t / along dendrites’ axis. 47) where gk is the conductance of the KC channel, gNa is the conductance of the NaC channel, and gL is the conductance of the leakage channel (Fig.
4 Phase Diagrams and Equilibria of Neuronal Models Fig. 7 Phase diagram of initial state variables x1 , x2 of a second order linear autonomous system with negative eigenvalues, where 1 < 2 <0 39 10 8 6 4 x2 2 0 −2 −4 −6 −8 −10 −15 Fig. 5 −2 −30 x1 Case 2: Complex eigenvalues: Typical phase diagrams in the case of stable complex eigenvalues are given in Fig. 10. Typical phase diagrams in the case of unstable complex eigenvalues are given in Fig. 11. Typical phase diagrams in the case of imaginary eigenvalues are given in Fig.