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

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.