Asymptotic stability of a modified Lotka-Volterra model with small immigration
Predator-prey systems have been well-studied in the field of mathematical biology because of their significance in analyzing the interaction of two species in a biological system. However, there is no existing mathematical model that explains an extremely stable coexistence of predators and preys. In a recent study co-authored by Dr. Maica Krizna A. Gavina, Dr. Jerrold M. Tubay, and Dr. Jomar F. Rabajante, they developed a mathematical model to describe a stable predator-prey system.
This research entitled Asymptotic stability of a modified Lotka-Volterra model with small immigration was published in Scientific Reports in 2018. They have shown that predators and preys can coexist if one adds a small number of immigrants to either population. They also compared these immigration cases with migration (-out) cases and found that either prey or predator population will become extinct. This shows that small immigrations invoke stable convergence in classical predator-prey systems. This means that natural predator-prey populations can be stabilized by a small number of sporadic immigrants.
For more details, check out https://doi.org/10.1038/s41598-018-25436-2.