Modeling a population of switches via chaotic dynamics

This note investigates the behavior of a population of interconnected irreversible switches, whose switching mechanism is triggered by a chaotic map. Motivation comes from the fact that many emergent properties of biological systems are ruled by the activation of a population of biochemical switches, whose timing and fluctuations may lead to different cell fates. They have been usually investigated according to a stochastic approach, and in this work we show how some properties could be similarly explained in terms of the emergent properties of a chaotic system. With respect to noise, chaos comes out from a deterministic framework, thereby allowing the implementation of experimental procedures directed to investigate the behavior of the system according to different scenarios by means of a rigorous deterministic passage from mathematics to simulation, that cannot be honestly rendered for the stochastic framework, since pseudo-random sequences are usually invoked.