The non-perturbative phenomenon for the Crow Kimura model with stochastic resetting

TL;DR

This paper investigates how stochastic resetting affects the Crow Kimura model, revealing a non-perturbative phase transition with two subphases when resetting to high fitness states, significantly altering the model's behavior.

Contribution

It introduces a modified Crow Kimura model with stochastic resetting and uncovers a non-perturbative phenomenon with phase substructure.

Findings

Resetting to low fitness states yields simple modifications of the standard model.

Resetting to high fitness states causes drastic, non-perturbative changes in the solution.

Two subphases are identified within the non-perturbative regime.

Abstract

We consider the Crow Kimura model, modified via stochastic resetting. There are two principally different situations: First, when due to resetting the system jumps to the low fitness state, everything is rather simple in this case, we have a solution which is a slight modification of the standard Crow-Kimura model case. When there is resetting to the high-fitness state, there is a non-perturbative phenomenon via the resetting probability, even a minimal resetting probability drastically changes the solution. We found two subphases in this phase.