By designing a proper electromagnetic constraint within a memristor, and introducing it into a dynamical system with the increase of dimension, a class of memristive chaotic systems with 2-D offset boosters is constructed. One offset constant directly applies offset boosting of a system variable while the other modifies the offset of two variables simultaneously. Furthermore, when the derived structure satisfies a specific feedback balance law, the property of total amplitude control can be obtained. The circuit implementation is consequently realized and the results are in line with the theoretical analysis.

Memristors have been widely integrated into neurons as the bridge for introducing external magnetic induction currents. The complex oscillation induced by the external magnetic stimulation is a hot topic in neuron dynamics. When a memristor is introduced into the Hindmarsh-Rose (HR) neuron to simulate the external magnetic field, a novel memristive neuromorphic hyperchaotic oscillator is constructed. The memristor weight can trigger complex neuronal firing dynamics, including the rare hyperchaotic bursting. Furthermore, when the technology of offset boosting-oriented attractor doubling is employed, a double-scroll hyperchaotic attractor can be generated, which could split into three independent coexisting attractors under some specific offsets. More interesting, two symmetric periodic attractors and two symmetric hyperchaotic attractors can coexist under certain conditions. In this work, a neuron with coexisting hyperchaotic attractors is constructed and exhaustively explored, which provides a good candidate for constituting large-scale brain-like neuromorphic oscillator. A PCB-based hardware circuit produces the oscillations validating the numerical simulations and theoretical analyses.

Memristors have been extensively studied in the field of nonlinear dynamics. However, the dynamic regulation mechanism of memristor-induced hyperchaotic oscillation has not been focused. In this article, a 5-D memristive hyperchaotic oscillator with amplitude control and uncountably many attractors reflecting the arbitrary relocation of the dynamics is constructed and analyzed. In this system, one parameter embedded in the memristor is responsible for partial amplitude control. An independent constant is applied for offset boosting with two system variables. Also, variable boosting can be achieved by varying the initial values, indicating that the system has homogenous multistability, which is shown to have uncountably many continuously distributed attractors. This memristive system provides the first example with uncountably many coexisting hyperchaotic attractors without any periodic function involved. Circuit implementation verifies the theoretical analysis and numerical simulations. A manganese electrolysis experiment was proposed to verify the unique advantage of offset-controllable hyperchaotic current in industrial electrolysis.