The Non-perturbative Phenomenon for the Crow Kimura Model with Stochastic Resetting

We consider the Crow Kimura model, modified via stochastic resetting. In our study, we examine the modified Crow–Kimura model with the introduction of stochastic resetting. We encounter two distinct scenarios: a. Resetting to Low Fitness State: In this case, the system transitions to a low fitness state due to resetting. The solution for this scenario resembles a slightly modified version of the standard Crow–Kimura model. b. Resetting to High Fitness State: Here, the system experiences a non-perturbative phenomenon involving the resetting probability. Even a minimal resetting probability leads to a significant alteration in the solution. Within this scenario, we identify two subphases. Our investigation delves into the interplay between stochastic resetting and the Crow–Kimura model, shedding light on how different types of resetting impact the behavior of the system.