DC-Offset Strategy for Controlling Hidden and Multistable Behaviors in Physical Circuits

Analog circuit detection of hidden and multistable dynamics is an intractable problem as their attraction basins are hard to locate rigorously in analog circuits. This article proposes a dc-offset strategy to achieve flexible control of hidden and multistable dynamics. A modified Chua's circuit with multiple dc control signals is constructed to demonstrate the feasibility of this dc-offset strategy. The kinetic effects of these dc control signals are systematically demonstrated. Then, taking the series dc voltage signal in the inductor branch as an example, the induced hidden and coexisting behaviors are detailed via theoretical analyses and numerical simulations. By introducing two dc voltage signals into the capacitor branches, the initial voltages of the two capacitors are accurately configured via predischarging the dynamic elements. The physical circuit is linearly reconstituted to make the attraction basins of desired coexisting attractors intersect with the easily implemented origin point. This improves the controllability of the hardware circuit and facilitates the analog circuit detection of hidden and coexisting dynamics. Hardware experiments are finally carried out to verify the feasibility of the dc-offset strategy.