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
A simplified hyperchaotic canonical Chua's oscillator (referred as SHCCO hereafter) made of only seven terms and one nonlinear function of type hyperbolic sine is analyzed. The system is found to be self-excited, and bifurcation tools associated with the spectrum of Lyapunov exponents reveal the rich dynamical behaviors of the system including hyperchaos, torus, period-doubling route to chaos, and hysteresis when turning the system control parameters. Wide ranges of hyperchaotic dynamics are highlighted in various two-parameter spaces based on two-parameter Lyapunov diagrams. The analysis of the hysteretic window using a basin of attraction as argument reveals that the SHCCO exhibits three coexisting attractors. Laboratory measurements further confirm the performed numerical investigations and henceforth validate the mathematical model. Of most/particular interest, multistability observed in the SHCCO is further controlled based on a linear augmentation scheme. Numerical results show the effectiveness of the control strategy through annihilation of the asymmetric pair of coexisting attractors. For higher values of the coupling strength, only a unique symmetric periodic attractor survives.