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.

The average value of a system variable determines the position of its attractor. When the offset parameters come together and get disappeared after an algebraic operation, the location of the attractor is then governed by an initial condition only. In this case, parameter-dominated offset control turns out to be the initial condition-defined coexisting attractors. In this Letter, a special mechanism for generating countless coexisting attractors is disclosed. Furthermore, a new regime of multistability is revealed, which explains where and how countless coexisting attractors are born and arranged.