Fractional Derivatives and Hopf Bifurcation in Ecological Interactions Among Plants, Pollinators, and Herbivores
摘要
Biological interactions and relationships between species are the basis of ecosystem balance, allowing their survival and coexistence, some favorable and others harmful. Some of these interactions, such as those between pollinators and plants or between herbivorous animals and plants are particularly interesting because they have environmental and socioeconomic impacts. Since Holling introduced functional response functions to describe predator-prey relationships, the mathematical modeling of these interactions has made remarkable progress, but traditional models based on integer differential equations have limitations, especially in incorporating memory effects and complex temporal dependencies. In this sense, fractional derivatives have emerged as a powerful tool allowing more precise descriptions of population dynamics and ecological interactions. This work proposes an innovative approach using fractional models to analyze plant-pollinator-herbivore interactions, offering a deeper perspective on the underlying mechanisms. In addition, we show numerical evidence of a Hopf bifurcation when the predator mortality parameter changes, which is interesting since this parameter can represent different predators and biological scenarios. This approach represents a significant advance in understanding ecological systems, contributing to the study of biodiversity and ecosystem sustainability.