Traveling wave solutions for a normalized time-fractional predator-prey model

초록

We introduce a normalized time-fractional diffusive predator-prey model that accounts for memory effects through a novel fractional time scale. Unlike conventional time-fractional models, the proposed formulation uses a normalized fractional derivative that ensures the total weight of the memory kernel remains unity, which enables a more consistent interpretation of historical influence across all fractional orders. The model is discretized using a finite difference scheme and solved via tridiagonal systems. Numerical simulations are performed to study traveling wave solutions and the dynamics of the system under varying fractional orders. The computational results demonstrate that decreasing the order of the fractional derivative leads to shorter temporal periods and increased spatial wavelengths in the predator-prey oscillations, while simultaneously reducing the amplitude of population fluctuations. These numerical experiments highlight the important role of fractional order in controlling the temporal and spatial evolution of ecological systems and emphasize the advantages of normalization in analyzing such dynamics.

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