Modification in the spatially extended Nicholson-Bailey host-parasitoid model with Coupled Map Lattice
DOI:
https://doi.org/10.35819/remat2022v8i1id5287Keywords:
Difference Equations, Nicholson-Bailey, Coupled Map Lattice, StabilityAbstract
Several population dynamics can be modeled using difference equations, with which time is considered discrete and the state variable is continuous. Among the most known discrete models, the Nicholson-Bailey one stands out for being one of the first to attempt to portray a host-parasitoid dynamics through difference equations. Although it has been used as the basis for the formulation of more complex models, the Nicholson-Bailey model, in its original format, presents unstable coexistence equilibrium for any set of parameters. Therefore, several modifications were proposed to make it closer to what is expected in nature. The present work aims to present the study of a modification in the Nicholson-Bailey model in two stages: the first one consists in inserting a density-dependent growth factor for the host population; the second, in adding the spatial distribution via the Coupled Map Lattice in the already modified model. From the equilibrium stability analysis and numerical simulations, results suggest that with the proposed modification the Nicholson-Bailey model presents stable coexistence equilibrium and the inclusion of space does not contribute to its destabilization. Furthermore, the spatial model exhibits several patterns depending on the choice of parameters, such as waves, spirals and crystalline structures.
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