Reproducing countless hidden attractors in a memristive system based on offset boosting

Offset control has attracted great research in recent years, and the introduction of special offset functions can produce homogenous multistability; however, the uncountably many attractors caused by offset boosting have not been focused. In this work, a 4D memristive chaotic model with uncountably many hidden attractors is designed. More interestingly, two-dimensional offset boosting can be achieved by a constant that simply switches the two variables of the offset by combining different initial values with the offset parameter. The offset parameters of variables are hidden when offset parameters cancel each other out; variable boosting can also be achieved only by varying initial conditions, which present a special regime of homogenous multistability with uncountably many continuously distributed attractors. This system provides the first example with uncountably many hidden attractors without any periodic function involved. Finally, the proposed memristive circuit with chaotic behavior is implemented through printed circuit board; circuit implementation agrees well with the numerical explorations and theoretical analysis.