RESUMEN
Understanding and characterizing multistabilities, whether homogeneous or heterogeneous, is crucial in various fields as it helps to unveil complex system behaviors and provides insights into the resilience and adaptability of these systems when faced with perturbations or changes. Homogeneous and heterogeneous multistabilities refer, respectively, to situation in which various multiple stable states within a system are qualitatively similar or distinct. Generating such complex phenomena with multi-scrolls from inherent circuits is less reported. This paper aims to investigate extreme multistability dynamics with homogeneous and heterogeneous multi-scrolls in two coupled resonant oscillators through a shunted Josephson junction. Analysis of equilibrium points revealed that the system supports both hidden and self-excited attractors. Various dynamical tools, including bifurcation diagrams, spectrum of Lyapunov exponents, and phase portraits, are exploited to establish the connection between the system parameters and various complicated dynamical features of the system. By tuning both system parameters and initial conditions, some striking phenomena, such as homogeneous and heterogeneous extreme multistability, along with the emergence of multi-scrolls, are illustrated. Furthermore, it is observed that one can readily control the number of scrolls purely by varying the initial conditions of the investigated system. A multi-metastable phenomenon is also captured in the system and confirmed using the finite-time Lyapunov exponents. Finally, the microcontroller implementation of the system demonstrates strong alignment with the numerical investigations.
RESUMEN
Achieving synchronization in coupled non-identical chaotic systems has been a difficult endeavor, and improving the stability of synchronization in such systems poses additional challenges. This research work addresses these challenges by identifying stable synchronization in coupled non-identical chaotic systems and enhancing its stability. The study explores chaotic attractors that arise from various system parameters to provide generalized results. Furthermore, the impact of the transient uncoupling factor on improving synchronization stability in coupled non-identical counter-rotating chaotic oscillators is discussed. By investigating these aspects, the research aims to contribute to the understanding and advancement of synchronization in coupled non-identical chaotic systems.