Traveling waves and their Stability for a Public Goods Game Model

TL;DR

This paper investigates the existence, uniqueness, monotonicity, asymptotic behavior, and stability of traveling wave solutions in a reaction-diffusion model of a public goods game with altruism, using mathematical analysis techniques.

Contribution

It introduces a rigorous analysis of traveling waves in a public goods game model, including existence, uniqueness, asymptotic behavior, and stability results.

Findings

Existence of traveling wave solutions established.

Traveling waves are unique and strictly monotonic.

Stability of non-critical speed waves demonstrated through spectral analysis.

Abstract

We study the traveling wave solutions to a reaction diffusion system modeling the public goods game with altruistic behaviors. The existence of the waves is derived through monotone iteration of a pair of classical upper- and lower solutions. The waves are shown to be unique and strictly monotonic. A similar KPP wave like asymptotic behaviors are obtained by comparison principle and exponential dichotomy. The stability of the traveling waves with non-critical speed is investigate by spectral analysis in the weighted Banach spaces.