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Target competition for resources under multiple search-and-capture events with stochastic resetting.

P C Bressloff1

  • 1Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, UT 84112, USA.

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|November 23, 2020
PubMed
Summary

We developed a framework to analyze resource distribution in target populations during search-and-capture events. Slowing down particle resets can optimize total resource delivery, enhancing search efficiency.

Keywords:
Green’s functionsdiffusionfirst passage timematched asymptoticssearch processesstochastic resetting

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Area of Science:

  • Mathematical Biology
  • Stochastic Processes
  • Search Theory

Background:

  • Understanding resource distribution is crucial in ecological and biological systems.
  • Previous models often lack the complexity to account for resetting search behaviors.

Purpose of the Study:

  • To develop a general framework for analyzing resource distribution under resetting search-and-capture events.
  • To investigate the impact of resetting frequency on resource allocation and total resource accumulation.

Main Methods:

  • Application of renewal theory to determine mean resource counts based on search splitting probabilities and first passage times.
  • Utilized asymptotic partial differential equation (PDE) methods for diffusive search in a 2D bounded domain with multiple targets.
  • Analysis of the effects of resetting on resource distribution and target competition.

Main Results:

  • Slow resetting increases total resources (M_tot) when a specific condition involving the Neumann Green's function and target locations is met.
  • The total number of resources can be optimized by adjusting the resetting rate (r).
  • A target gains a competitive advantage if its location satisfies a particular mathematical criterion.

Conclusions:

  • The study provides a theoretical framework for optimizing resource delivery through controlled search-and-capture dynamics.
  • Resetting parameters significantly influence resource distribution and can be tuned for maximum efficiency.
  • Identified conditions for competitive advantage among targets, relevant for understanding population dynamics.