Coexistence of hyperchaos with chaos and its control in a diode-bridge memristor based MLC circuit with experimental validation
Théophile Fonzin Fozin, Bernard Koumetio Nzoko, Nicole Adelaïde Kengnou Telem, Zeric Tabekoueng Njitacke, Adele Armele Ngo Mouelas, Jacques Kengne
Abstract
Abstract This paper reports both the coexistence of chaos and hyperchaos and their control based on a noninvasive temporal feedback method for attractor selection in a multistable non-autonomous memristive Murali-Lakshamanan-Chua (MLC) system. Numerical simulation methods such as bifurcation diagrams, the spectrum of Lyapunov exponents, phase portraits, and cross-section basins of initial states are used to examine several striking dynamical features of the system, including torus, chaos, hyperchaos, and multistability. Of most interest, the rare phenomenon of the coexistence of hyperchaos and chaos has been uncovered based on bifurcation techniques and nonbifurcation scheme like offset boosting. Further analyses based on intermittent feedback-based control in the time domain help to drive the system from the multistable state to a monostable one where only the hyperchaotic attractor survives. Since the attractor’s internal dynamics are retained, this control method is non-invasive. At the end of our analyses, the results of both PSpice and that of the microcontroller-based digital calculator of the circuit match perfectly with the numerical investigations.