Chaos, periodic structures, and multistability: Complex dynamical behaviors of an eco-epidemiological model in parameter planes.

Abstract

The environmental characteristics of a biological system are imbibed in some particular parameters of that system. Significant changes in any system parameter exert influence on the system dynamics as well as the persistence of interacting species. In this article, we explore the rich and tangled dynamics of an eco-epidemiological system by studying different parametric planes of the system. In the parameter planes, we find a variety of complex and subtle properties of the system, like the presence of a variety of intricate regular structures within irregular regimes, that cannot be found through a single parameter variation. Also, we find a new type of structure like an "eye" in a parametric plane. We notice the bistability between distinct pairs of attractors and also identify the coexistence of three periodic attractors. The most notable observation of this study is the coexistence of three periodic attractors and a chaotic attractor, which is a rare occurrence in biological systems. We also plot the basins for each set of coexisting attractors and see the existence of fractal basins in the system, which look like a "conch." The appearance of fractal basins in a system causes enormous complications in predicting the system's state in the long run. Variations in initial conditions and changes in parameters in parametric planes are key to managing the behavior of a system.