Global entrainment of transcriptional systems to periodic inputs

TL;DR

This paper uses contraction theory to establish conditions under which transcriptional systems globally entrain to periodic inputs, ensuring all solutions converge to a limit cycle, with proofs and applications to biological models.

Contribution

It provides new mathematical conditions for global entrainment in transcriptional systems using contraction theory, with a self-contained proof framework.

Findings

Systems driven by periodic signals exhibit convergence to a limit cycle.

General mathematical results for contraction theory are established and verified.

Application to specific transcriptional models demonstrates practical relevance.

Abstract

This paper addresses the problem of giving conditions for transcriptional systems to be globally entrained to external periodic inputs. By using contraction theory, a powerful tool from dynamical systems theory, it is shown that certain systems driven by external periodic signals have the property that all solutions converge to a fixed limit cycle. General results are proved, and the properties are verified in the specific case of some models of transcriptional systems. The basic mathematical results needed from contraction theory are proved in the paper, making it self-contained.