Existence of Traveling Waves of Lotka Volterra Type Models with Delayed Diffusion Term and Partial Quasimonotonicity
Abstract
Abstract This paper investigates the existence of traveling wave solutions for diffusive two-species Lotka–Volterra systems with delays in both the reaction and diffusion terms under partial monotonicity assumptions. The model incorporates small-memory effects in the homogeneous diffusion term, representing a modification of the random-walk interpretation underlying Fick’s law. We extend the partial (cross) monotone iteration method to systems satisfying a partial quasi-monotone condition through the construction of appropriate upper and lower solutions. Convergence of the iteration is established using Schauder’s fixed point theorem.
Fields of Study & Subjects
Mathematical and Theoretical Epidemiology and Ecology Models
Fractional Differential Equations Solutions
Publication details
- Journal / source
- International Journal of Applied and Computational Mathematics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 12
- Issue
- 3
- Publication date
- 4 May 2026
- Language
- EN