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A simple variable-boostable system is selected as the structure for hosting an arbitrarily defined memristor for chaos producing. The derived three-dimensional (3-D) memristive chaotic system shows its distinct property of offset, amplitude and frequency control. Owing its merits any desired number of coexisting attractors are embedded by means of attractor doubling and self-reproducing based on function-oriented offset boosting. In this circumstance two classes of control gates are found: one determines the number of coexisting attractors resorting to the independent offset controller whil the other is the initial condition selecting any one of them. Circuit simulation gives a consistent output with theoretically predicted embedded attractors.

Offset boosting is an important issue for chaos control due to its broadband property and polarity control. There are two main approaches to realize offset boosting. One is resort to parameter introducing where an offset booster realizes attractor boosting. The other one is by the means of periodic function or absolute value function where any self-reproduced or doubled attractors with diverse offset are extracted out by a specific initial condition. The former also provides a unique window for observing multistability and the latter gives the direction for constructing desired multistability.