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Based on a variable-boostable chaotic system, a conservative chaotic system with controllable amplitude and offset is proposed. The system exhibits rich symmetrical dynamics under different parameters and initial conditions. More interestingly, a parameter of memristor poses a partial amplitude control to a system variable. Furthermore, the derived memristive system has the property of offset boosting, where an independent constant can be introduced for free rescaling of the average value of a system variable. Experimental circuit with a memristor rheostat is designed for amplitude control. Circuit simulation based on Multisim software agrees well with the systematic analysis and numerical exploration. To the best of our knowledge, in the literature there is no 3D conservative memristive system reported with such properties as amplitude control and offset boosting.

The fundamental dynamics of the deformed Rikitake two-disc dynamo system is explored in this paper. Memory effect on the dynamical behavior of the generator system is studied by introducing a quadratic flux-controlled memristor. Hyperchaotic oscillation in the deformed Rikitake two-disk coupled generator is therefore firstly found. Lyapunov exponents, bifurcation diagram, and phase portraits prove the abundant dynamic behavior consistently.

An amplitude controllable hyperjerk system is constructed for chaos producing by introducing a nonlinear factor of memristor. In this case, the amplitude control is realized from a single coefficient in the memristor. The hyperjerk system has a line of equilibria and also shows extreme multistability indicated by the initial value-associated bifurcation diagram. FPGA-based circuit realization is also given for physical verification. Finally, the proposed memristive hyperjerk system is successfully predicted with artificial neural networks for AI based engineering applications.

A generalized memristor is introduced in Liu-Chen chaotic system for amplitude control. Different from other chaotic systems, the oscillation behavior can be rescaled in amplitude and frequency by three independent controllers. One controls the amplitude of two related variables, and the other two control both amplitude and frequency of some variables. More distinctively, the proposed memristive chaotic system shows abundant coexisting pairs of attractors under the condition of broken symmetry. The circuit experiment based on Multisim agrees with the numerical exploration.