<title>Studies on a network of complex neurons</title>

Abstract

In the last decade, much effort has been directed towards understanding the role of chaos in the brain. Work with rabbits reveals that in the resting state the electrical activity on the surface ofthe olfactory bulb is chaotic. But, when the animal is involved in a recognition task, the activity shifts to a specific pattern corresponding to the odor that is being recognized. Unstable, quasiperiodic behavior can be found in a class of conservative, deterministic physical systems called the Hamiltonian systems. In this paper, we formulate a complex version of HopfIeld's network of real parameters and show that a variation on this model is a conservative system. Conditions under which the complex network can be used as a Content Addressable memory are studied. We also examine the effect of singularities of the complex sigmoid function on the network dynamics. The network exhibits unpredictable behavior at the singularities due to the failure of a uniqueness condition for the solution of the dynamic equations. On incorporating a weight adaptation rule, the structure of the resulting complex network equations is shown to have an interesting similarity with Kosko's Adaptive Bidirectional Associative Memory.3 SOME PROPERTIES OF THE COMPLEX HOPFIELD NETWORK Lemma 1 LeL z = x + ij and g(z) g + igy tanh(z). Then, 1. >Ofor-ir/4<y<ir/4. . gl*(z) = SPIE Vol. 1966 Science of Artificial Neural Networks 11(1993) / 31 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/15/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Ui Uzi Uzj for u = 0 and u = nr + SPIE Vol. 1966 Science of ArLificial Neural Networks 11(1 993) / 37 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/15/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx