Multiple coexisting attractors and self-organized distribution of periodicity in a three-dimensional system.

In chemical reactions, autocatalator models hold a significant place for exhibiting different kinds of complex dynamical features. The present study focuses on the dynamical characterization of a three-variable autocatalator model in a parameter plane. A detailed analysis is performed on the distribution of dynamically rich and complex oscillatory states in the system by forming a few Lyapunov exponent and isoperiodic diagrams. Regular organization of familiar periodic structures, including shrimp-shaped islands and Arnold tongues, is found in the chaotic and quasiperiodic zones of the parameter plane. A comprehensive discussion on two different kinds of multistability, viz., bistability and tristability, is also provided. It is observed that the basin boundary of the two coexisting attractors is smooth, whereas that of the three coexisting attractors is partially fractal in nature. Through this study, we gain a deeper perception of the intricate dynamics of the present system, resulting from simultaneous changes in two control parameters.