Hidden Attractors in a Delayed Memristive Differential System with Fractional Order and Chaos Synchronization

As an important research branch, memristor has attracted a range of scholars to study the property of memristive chaotic systems. Additionally, time-delayed systems are considered a significant and newly-developing field in modern research. By combining memristor and time-delay, a delayed memristive differential system with fractional order is proposed in this paper, which can generate hidden attractors. First, we discussed the dynamics of the proposed system where the parameter was set as the bifurcation parameter, and showed that with the increase of the parameter, the system generated rich chaotic phenomena such as bifurcation, chaos, and hypherchaos. Then we derived adequate and appropriate stability criteria to guarantee the system to achieve synchronization. Lastly, examples were provided to analyze and confirm the influence of parameter a, fractional order q, and time delay τ on chaos synchronization.The simulation results confirm that the chaotic synchronization is affected by a,q and τ.