Adaptive Synchronization for Hyperchaotic Liu System

In this paper, the adaptive control design is investigated for the chaos synchronization of two identical hyperchaotic Liu systems. First, an adaptive control law with two inputs is proposed based on Lyapunov stability theory. Secondly, two other control schemes are obtained based on a further analysis of the proposed adaptive control law. Finally, numerical simulations are presented to validate the effectiveness and correctness of these results.

Study on Quasi-Period and Chaos Synchronizations of a Laser Local Area Network by Shifting the Currents of One Chain Node Lasers

Quasi-period and chaos synchronizations of a laser local area network (LAN) are discussed deep by shifting or controlling the current parameters of one chain node lasers of the LAN. The two coupling-lasers as network’s double-driver nodes and other two laser as network’s receiver node lasers perform two chains of laser LAN. Multi-dynamics states and their synchronizations, such as quasi-period, chaos and their synchronizations, are guided to show in the LAN by varying the current parameters of one chain node lasers. We find that multi-dynamics state synchronizations, such double-period, period-3, period-4, period-5, other quasi-period and chaos synchronizations, are guided to present at two chains of the LAN. This LAN and its obtained results have import reference values for complex system, network, artificial intelligence, chaos synchronization.

Results for Chaos Synchronization with New Multi-Fractional Order of Neural Networks by Multi-Time Delay

A new finding is proposed for multi-fractional order of neural networks by multi-time delay (MFNNMD) to obtain stable chaotic synchronization. Moreover, our new result proved that chaos synchronization of two MFNNMDs could occur with fixed parameters and initial conditions with the proposed control scheme called sliding mode control (SMC) based on the time-delay chaotic systems. In comparison, the fractional-order Lyapunov direct method (FLDM) is proposed and is implemented to SMC to maintain the systems’ sturdiness and assure the global convergence of the error dynamics. An extensive literature survey has been conducted, and we found that many researchers focus only on fractional order of neural networks (FNNs) without delay in different systems. Furthermore, the proposed method has been tested with different multi-fractional orders and time-delay values to find the most stable MFNNMD. Finally, numerical simulations are presented by taking two MFNNMDs as an example to confirm the effectiveness of our control scheme.