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.

In this work, the study of an innovative chaotic system made from two memristors with symmetric bifurcation and multistability is presented. Within a four dimensional chaotic framework, the system is architected with two flux controlled memristors. Computational simulations reveal intricate dynamical phenomena such as symmetric bifurcations, multistability, and very large sensitivity to initial conditions. Using Lyapunov exponents, bifurcation diagrams and phase portraits, we investigate the system's ability to produce chaotic attractors of pronounced multistability. Pinched hysteresis loop and system offset investigation at different frequencies are investigated for possible applications in neuromorphic computing, random number generation and secure communication protocols. We further advance our understanding of the complex dynamical properties of memristive chaotic systems. A representative analog circuit corroborates their numerical findings.

Offset boosting and amplitude control of chaos play an important role in chaos-based engineering applications. In this work, a simple 4D chaotic oscillator is designed with three independent offset boosters that provide a single control, synchronous reverse control, and even differential control. Moreover, the offset level of the related variables is also closely associated with one of the bifurcation parameters. More strikingly, there is a global amplitude controller in this system that can rescale all the variables combined with any regime of offset boosting. Finally, a compact and simple chaotic circuit is designed, containing only a multiplier, two operational amplifiers and a few capacitors and resistors, confirming the new properties of the oscillator.

In this article, an autonomous memristive hyperchaotic system with multi-dimensional offset boosting is constructed and analyzed. Besides this, the oscillation can be rescaled by an independent controller in the memristor. Two independent constants are obtained for offset boosting with one or two variables, which provide two modes of offset boosting, including single control and synchronous reverse control. In addition, the offset of the variables is also modified by the system bifurcation parameters or combined with amplitude control. The multistability can also be identified according to the offset boosting. Finally, circuit implementation based on PCB is proposed to confirm the numerical simulations.

By introducing a simple feedback, a hyperchaotic hidden attractor is found in the newly proposed Lorenz-like chaotic system. Some variables of the equilibria-free system can be controlled in amplitude and offset by an independent knob. A circuit experiment based on Multisim is consistent with the theoretic analysis and numerical simulation.