From Lévy to Brownian: A Computational Model Based on Biological Fluctuation

Abstract

BackgroundTheoretical studies predict that Lévy walks maximizes the chance of encountering randomly distributed targets with a low density, but Brownian walks is favorable inside a patch of targets with high density. Recently, experimental data reports that some animals indeed show a Lévy and Brownian walk movement patterns when forage for foods in areas with low and high density. This paper presents a simple, Gaussian-noise utilizing computational model that can realize such behavior.Methodology/Principal FindingsWe extend Lévy walks model of one of the simplest creature, Escherichia coli, based on biological fluctuation framework. We build a simulation of a simple, generic animal to observe whether Lévy or Brownian walks will be performed properly depends on the target density, and investigate the emergent behavior in a commonly faced patchy environment where the density alternates.Conclusions/SignificanceBased on the model, animal behavior of choosing Lévy or Brownian walk movement patterns based on the target density is able to be generated, without changing the essence of the stochastic property in Escherichia coli physiological mechanism as explained by related researches. The emergent behavior and its benefits in a patchy environment are also discussed. The model provides a framework for further investigation on the role of internal noise in realizing adaptive and efficient foraging behavior.

A Multi-Verse Optimizer with Levy Flights for Numerical Optimization and Its Application in Test Scheduling for Network-on-Chip

“…For exploring unknown, large-scale search spaces, Levy flights are superior to Brownian random walks [20, 26]. …”

Guided Self-Organization in a Dynamic Embodied System Based on Attractor Selection Mechanism

“…The GSO approach proposed in the manuscript is based on a coupling between the mechanical dynamics of an embodied system and a control structure known as attractor selection mechanism [11,12,[17][18][19][20]. The mechanism is inspired from a noise-utilizing behavior found in various scales of biological systems like stochasticity in molecular motors, cell signaling processes, dynamic structure of proteins and recognition in brains [11,12].…”

“…The mechanism is inspired from a noise-utilizing behavior found in various scales of biological systems like stochasticity in molecular motors, cell signaling processes, dynamic structure of proteins and recognition in brains [11,12]. Based on the observed dynamics, a simple model was proposed to explain the underlying mechanism by using a dynamical system equation with some attractors [12,[17][18][19][20]. The model was referred to as the attractor selection mechanism (ASM) and represented by Langevin equation as: The potential function U(t) can be designed to have some attractors.…”

“…Most recently, it is reported that Levy walks in mussels should have evolved through interaction with their environment [16]. Several studies have also been dedicated to understand and model the balance between stochastic behavior in biological systems commonly measured by entropy, and the ability to attenuate the effect of the randomness to reveal potentially useful deterministic dynamics [11][12][13][17][18][19][20].…”

“…The approach taken is to use a mathematical framework known as attractor selection mechanism as the control structure [11,12,[17][18][19][20]. It is hypothesized that by coupling the mechanical dynamics of the body properly with the mechanism, the corresponding embodied system should be able to gracefully switch between random and deterministic behaviors.…”