Stability and chaos in coupled two-dimensional maps on Gene Regulatory Network of bacterium E.Coli

TL;DR

This paper explores how coupled chaotic maps on the E.Coli gene regulatory network exhibit stable, coherent, and self-organized dynamics depending on coupling strength and network topology.

Contribution

It investigates the collective dynamics of coupled two-dimensional maps on a biological network, revealing how coupling influences stability and chaos.

Findings

Stable and coherent dynamics emerge at low coupling strengths.

Unstable behavior remains confined within parts of the network at higher coupling.

The network shows robust self-organized dynamics in a weakly chaotic regime.

Abstract

The collective dynamics of coupled two-dimensional chaotic maps on complex networks is known to exhibit a rich variety of emergent properties which crucially depend on the underlying network topology. We investigate the collective motion of Chirikov standard maps interacting with time delay through directed links of Gene Regulatory Network of bacterium Escherichia Coli. Departures from strongly chaotic behavior of the isolated maps are studied in relation to different coupling forms and strengths. At smaller coupling intensities the network induces stable and coherent emergent dynamics. The unstable behavior appearing with increase of coupling strength remains confined within a connected sub-network. For the appropriate coupling, network exhibits statistically robust self-organized dynamics in a weakly chaotic regime.