Dynamical behavior of obligatory mutualistic-cheater interactions under the influence of white noise

Intraspecific mutualism is vital for ecosystems. Some interactions involve one species benefiting without reciprocating. Recent experiments suggest stable co-existence between mutualists and cheaters. This paper focuses on interactions between obligate mutualistic species and their cheaters, using a modified Lotka-Volterra model to analyze the negative impact of cheaters. We establish conditions for stability and verify a diffusive system's stability under spatial effects. Additionally, we study population dynamics fluctuations in the presence of Gaussian noise.