Global dynamics of a one-predator-two-prey model and its traveling wave solutions

• Published in: Mathematics in applied sciences and engineering Vol. 6; no. 3; pp. 238 - 256
• Main Authors: Yang, Yung-Chih, Lin, Jian-Jhong, Yang, Tinghui
• Format: Journal Article
• Language: English
• Published: Western Libraries 01.09.2025
• Subjects: Two-prey-one-predator models, global dynamics, traveling wave solutions, Wazewski principle
• ISSN: 2563-1926; 2563-1926
• DOI: 10.5206/mase/21285

This work investigates the three species of one-predator-two-prey ecological models in Lotka-Volterra type functional response with or without diffusive terms. Without the diffusive effects and under two essential assumptions, we can generically classify all global dynamics completely. The global asymptotic stabilities of three equilibria are shown analytically in each case. Alternatively, with the diffusive term, we establish the existence of traveling wave solutions by the higher-dimensional shooting method, the Wazewski principle. In particular, there are two critical wave speeds $0<c_2<c_1$. We show the existence of traveling wave solutions with the wave speed $c$ if $c>c_1$ and the non-existence of traveling wave solutions if $0<c<c_2$. Finally, a brief discussion, biological interpretations, and numerical simulations are given.