Organized structures and different types of multistability in a one-dimensional ecological model — A parameter plane study

Abstract

In this article, we present an in-depth investigation of the parameter plane of a one-dimensional ecological model, highlighting the existence of intriguing dynamical scenarios and organized structures even in a rather simple ecological model. Specifically, we report the discovery of a fish-like periodic structure with period one surrounded by an unbounded region and numerous shrimp-shaped structures for the first time within the parameter plane of a one-dimensional ecological map. We uncover diverse dynamical phases in the parameter plane using isoperiodic diagrams and Lyapunov exponent diagrams. Our analyses reveal both period-doubling and period-bubbling cascades. We also observe the prevalence of various types of homogeneous and heterogeneous multistability phenomena. The most notable finding of the present study is the emergence of chaos–chaos multistability, characterized by the coexistence of two distinct chaotic attractors. Additionally, we identify a qualitatively different form of chaotic behavior referred to as multi-state intermittency, in which trajectories switch intermittently between two distinct fixed points rather than settling around a single fixed point. The insights gained from this study will significantly improve the understanding of complex and nuanced dynamical scenarios present in the parameter plane of one-dimensional ecological models, and provide a foundation for exploring and visualizing similar dynamical scenarios in higher-dimensional ecological models.