A Novel Method for Designing Multistable Systems with a Hidden Attractor

Dynamical systems with chaotic attractors are an interesting topic not only for their complex behavior but also due to their potential applications. Along with the chaos, systems can also present interesting features such as multistability, global basin of attractions, entangled basins of attraction, etc. The existence of chaotic systems with multistable hidden attractors increases complexity but also the number of potential applications. Several systems with hidden attractors have already been found by numerical search; however, it is usually not possible to substantially modify their equations or attractor geometry. In this study, an approach to generate multistable systems with a class of hidden attractors is proposed. The approach allows for the control of the amplitude and frequency of the chaotic signals of the different attractors as well as their location in the space by preserving a simple matrix form in the vector field. Particular cases with mono-stability and multistability are shown. Also, chaotic signals obtained through the approach are used in a pseudorandom number generator to obtain binary sequences which are tested under the Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications provided by the National Institute of Standards and Technology (NIST).