A Deterministic Model for Harmful Algal Bloom (HAB) Patterns Under Turing’s Instability Perspective

Turing’s instability has been widely introduced to explain the formation of several biological and ecological patterns, such as the skin patterning of fish or animals, wings of butterflies, pigmentation, and labyrinth patterns of the cerebral cortex of mammals. Such a mechanism may occur in the ecosystem due to the differential diffusion dispersal that happen if one of the constituent species results in the activator or the prey, showing a tendency to undergo autocatalytic growth. The diffusion of the constituent species activator is a random mobility function called passive diffusion. If the other species in the system (the predator/inhibitor) disperses sufficiently faster than the activator, then the spatially uniform distribution of species becomes unstable, and the system will settle into a stationary state. This paper introduced Turing’s mechanism in our reaction–taxis–diffusion model to simulate the harmful algal bloom (HAB) pattern. A numerical approach, the Runge–Kutta method, was used to deal with this system of reaction–taxis–diffusion equations, and the findings were qualitatively compared to the aerial patterns obtained by a drone flying over Torment Lake in Nova Scotia (Canada) during the bloom season of September 2023.