A Mathematical Model of Tritrophic Systems

Lotoka—Volterra, LV equations are to model predator—prey problem. In principle, the LV equations are belongs to a two-person system. Even if there are many-body, it is structurally in two-body, i.e., with three or more predators and a prey. On the other hand, chemical ecology has shown that plants damaged by predation produce information chemicals (Hervibore Induced Plant Volatile, HIPV) that attract natural enemies. Chemical ecology suggests that the ecosystem is a tri-trophic system consisting of predator—plant (HIPV)—prey. Therefore, chemical ecosystems are essentially different from LV equations. This paper proposes a basic equation for tri-trophic systems and investigates their stability.