[Turkmath:6846] Applied Dynamics Group Seminar

[M. Onur Fen]

Dear all,

You are cordially invited to the seminar entitled "Analysis of neural
networks with piecewise constant argument of generalized type" which will
be given by Enes Yilmaz, from Institute of Applied Mathematics, METU.

ABSTRACT:
       In this talk, we discuss recurrent neural networks (RNNs): 
Hopfield neural networks (HNNs) and Cellular neural networks (CNNs)
with piecewise constant  arguments  [1-4]. These networks have been
extensively studied in recent years due to their applicability in
solving associative memory, image and signal processing, pattern
recognition and so on.  As it is well known, applications of RNNs
depend crucially on the dynamical behavior of the networks.
 	In the first part of talk, we describe the structure of biological
neurons and artificial neuron model proposed by McCulloch and Pittz.
Next, sufficient conditions ensuring the existence, uniqueness and
global stability of equilibrium point for RNNs will be discussed. In
papers [1-4], we propose the stability criterion based on linearization.
Unlike these papers, the stability was analyzed by the second Lyapunov
method in [5]. Nevertheless, it is the first time that the second method
is applied to RNNs,  arguments of which are not only delayed but also
advanced in [4]. Finally, we present numerical simulations to illustrate
the results. Since the equation is of mixed type (advanced-delayed), the
numerical analysis has a specific character.  It is in full accordance
with the approximations made in proofs of theorems. This important that
the non-smoothness of solutions expected from the equations’ nature is
also seen.

References

[1]  M. U. Akhmet and  E. Yilmaz, Hopfield type neural network systems
with piecewise constant argument,  Inter. Jour. of Qual. Theory of Diff. 
Eqns.  and App. Vol. 3, No. 1-2 (2009)  8–14.
[2]  M. U. Akhmet, E. Yilmaz,  Impulsive Hopfield type neural network
systems with piecewise constant argument, Nonlinear Anal.: RWA.,  (In
Press).
[3]  M. U. Akhmet, D. Arugaslan and E. Yilmaz, Stability in cellular
neural networks with  piecewise constant argument,  J. Comput. Appl.
Math., 233 (2010) 2365-2373.
[4]  M. U. Akhmet, D. Arugaslan and E. Yilmaz, Stability analysis of
recurrent  neural networks with  piecewise constant argument of
generalized type, (Submitted for publication).
 [5]  M. U. Akhmet, D. Arugaslan and E. Yilmaz,  Method of Lyapunov
functions for differential equations with piecewise constant delay, J.
Comput. Appl. Math.,  (In Press).


DATE :  19.03.2010
TIME :  15:00
PLACE : Gunduz Ikeda Seminar Room

Best regards,

Mehmet Onur Fen