Logistic networks with DNA-like encoding and interactions

Abstract

We consider a logistic network consisting of a coupled population of externally driven logistic processing elements (LPEs) or “neurons” with quantized interactions between them. The interactions are modeled after the encoding of genetic information in molecular biology, i.e. as in DNA molecules in terms of four nucleotide bases. A unique and versatile scheme for generating complex spatio-temporal input patterns to drive the network, that could contain chaotic components, is employed to study the network's behavior. Both coherent (phase-locked) and incoherent input patterns can be generated. We find that DNA-like encoding of interactions causes quantization and clustering to appear in the activity of the network which we represent by limit-set-diagrams (LSDs). Clustering means grouping of processing elements into subpopulations with period-m orbits where m is constant for each cluster, but the values of m are different for different clusters. The clustering is found to characterize the particular input pattern being applied to the network, it changes gradually with gradual change in the input, and appears to persist even when the input pattern contains chaotic components. A striking similarity of bifurcation diagrams of isolated driven LPEs and of the LSDs generated to the bar patterns observed in gel-electropheresis of oligonucleotides and DNA fragments is observed. This could portend a useful link to molecular biology and serve as basis for introducing a molecular computing paradigm in neural networks.

An oligonucleotide is a short chain of nucleotide. It is a synthetic single stranded DNA molecule that is made with a chosen sequence of nucleotides selected from the four nucleotide bases G,C,T,A [14]. In the logistic net described here, the four nucleotide bases are replaced by the four numbers 1,2,3,4 and the oligonucleotide-like sequences produced, designated O_i ^s(n) and O_ij(n), have elements selected from the set 1,2,3,4 equivalent to the four nucleotide bases in molecular biology.