# The strategy of survival for a competition between normal and anomalous diffusion

## TL;DR

This paper investigates the competition between normal and anomalous diffusion processes, revealing how memory effects in anomalous diffusion can be strategically used to prolong survival in competitive scenarios.

## Contribution

It introduces a model analyzing how anomalous diffusion with memory can adapt strategies to survive against faster normal diffusion in various real-world competitions.

## Key findings

- Anomalous diffusion can outperform normal diffusion by strategic memory management.
- Memory loss in anomalous diffusion enhances its survival prospects.
- The model applies to markets, epidemics, and ecological competitions.

## Abstract

In this paper, we study the competition of two diffusion processes for achieving the maximum possible diffusion in an area. This competition, however, does not occur in the same circumstance; one of these processes is a normal diffusion with a higher growth rate, and another one is an anomalous diffusion with a lower growth rate. The trivial solution of the proposed model suggests that the winner is the one with the higher growth rate. But, the question is: what characteristics and strategies should the second diffusion include to prolong the survival in such a competition? The studied diffusion equations correspond to the SI model such that the anomalous diffusion has memory described by a fractional order derivative. The strategy promise that anomalous diffusion reaches maximum survival in case of forgetting some parts of the memory. This model can represent some of real phenomena, such as the contest of two companies in a market share, the spreading of two epidemic diseases, the diffusion of two species, or any reaction-diffusion related to real-world competition.