A random walk model to study the cycles emerging from the exploration-exploitation trade-off

TL;DR

This paper introduces a memory-based random walk model inspired by biological systems, demonstrating how exploration-exploitation strategies can lead to emergent cycles in the system.

Contribution

It presents a novel random walk model incorporating memory effects and explores how different strategies induce emergent cyclic behaviors.

Findings

Memory influences walker's movement probabilities.

Emergence of cycles from exploration-exploitation dynamics.

Different strategies lead to distinct behavioral patterns.

Abstract

We present a model for a random walk with memory, phenomenologically inspired in a biological system. The walker has the capacity to remember the time of the last visit to each site and the step taken from there. This memory affects the behavior of the walker each time it reaches an already visited site modulating the probability of repeating previous moves. This probability increases with the time elapsed from the last visit. A biological analog of the walker is a frugivore, with the lattice sites representing plants. The memory effect can be associated with the time needed by plants to recover its fruit load. We propose two different strategies, conservative and explorative, as well as intermediate cases, leading to non intuitive interesting results, such as the emergence of cycles.