Stabilization of the homogeneous multistability in a memristive system

When a memristor is introduced to the chaotic system with amplitude and frequency control, a new regime of homogeneous multistability could be induced, where the initial condition could extract the chaotic oscillation with different levels of amplitude and frequency, which shows great potential for applications such as data encryption, communication, and intelligent control. However, some chaotic systems with undesired growth of amplitude and frequency may trigger instability or even bring catastrophic failure. In this work, two amplitude-frequency stabilization methods are proposed for suppressing such kind of homogeneous multistablity: one is resort to hardware saturation for limiting the growth of the inside variable of the memristor, while the other one depending on the introducing of negative feedback to realize dynamical control. Both methods effectively inhibit the amplitude-frequency growth of chaotic oscillation, which can be adapted to control the amplitude and frequency even when the symmetry is broken. The mechanism of countless coexisting attractors in the system is also disclosed. Practical circuits verify the feasibility and robustness of the stabilization method. In addition, it is found that the periodic modulation of chaotic variables can be realized by introducing a memory-damped electromagnetic constraint within a finite value domain, which provides a new schematic for subsequent chaotic communication.