Український математичний конгрес - 2009

Alexander Glushkov (Odessa State University OSEU, Odessa, Ukraine)

Dynamics of multi-layers neural networks on the basis of photon echo: Effects of chaos and stochastic resonance

In our work we carry out new quantum models for dynamics of the optical neural networks on the basis of the photon echo and study the features of the optical bi-stability manifestation, resonance-stochastic effects in two-level atomic ensembles [1] and provide the PC computer realization of the models with the aim of computer modelling the neural networks dynamics [2]. We proposed a new quantum model of optical photon echo neural networks, provided by hyperfine structure of states of the two-level atomic ensembles. The results of the computer experiments on dynamics of neural networks with input rectangular pulse are presented. On the basis of the object oriented programming we carried out the numerical realization of the new model and performed the computer simulation experiments in order to study the optimal information possibilities of photon echo neural network in tasks of the images and complex signals detection and estimate a possibility of the resonance stochastic effects manifestation. In particular, the input signal is modelled by the sin, cos , soliton-like, rectangular pulses. Besides, it has been considered a case of the noise input signal sequence. It is shown that for definite value of the additive noise intensity D ( D = 0,0001-0,004) a tutoring process of the neural network is very effective and the signal reproduction is an optimal (the optimal value D = 0,0017). A coherence of input and output is optimal under definite level of noise. So, it is shown that it is possible a realization of the stochastic resonance regime in a photon echo neural networks system.

[1] A. Glushkov, et al, Recent Adv. in Theory of Phys.and Chem. Systems (Berlin, Springer) 15:285-300, 2006.
[2] A.V. Glushkov, A.V.Loboda, A.A. Svinarenko, Dynamics of neural networks on basis of photon echo and its computer program realization, Odessa: TEC, 2004; 300p.
[3]. V.D. Rusov, A.V. Glushkov, A.A. Svinarenko et al, Advances in Space Research. 42:1614-1617 (2008).