Structural sensitivity of a tri-trophic food chain model in a parameter plane

Biological models are important in describing species interaction, disease spread, and environmental processes. One key aspect in improving the predictive capability of these models is deciding which parametrization is used to formulate the mathematical model. Considering two distinct functions with similar shapes and the same qualitative properties in a model can lead to markedly different model predictions. Such a phenomenon is recognized as the structural sensitivity of models. In this article, we investigate the structural sensitivity of a tri-trophic food chain model in a parameter plane by considering three nearly indistinguishable forms of the trophic function, namely, Holling type-II, Ivlev, and trigonometric. We use various tools, including bifurcation diagrams, isospike diagrams, and Lyapunov exponent diagrams, to explore the structural sensitivity of the model. The findings show that a functional form has a significant impact on the organization of periodic structures in the parameter plane. The model exhibits a range of diverse dynamics in a fixed parameter range with variations in the functional form. The survival of species and the nature of oscillations are heavily influenced by the model's constituent functions. Our results suggest that even slight variations in the functional response curves can lead to significant differences in the qualitative and quantitative dynamics of a food chain model.