Hybrid synchronization of coupled fractional-order complex networks

Adaptive Event-Triggered Lag Outer Synchronization for Coupled Neural Networks With Multistate or Multiderivative Couplings

Multistate coupled coupled neural networks (MSCCNN) and multiderivative coupled coupled neural networks (MDCCNN) are introduced in this article, and the lag outer synchronization for these two networks are tackled. First, a lag outer synchronization criterion for MSCCNN is derived using a node-based adaptive event-triggered control scheme, and the fact that the Zeno behavior does not exist is also proved. Moreover, the edge-based adaptive event-triggered control method is also utilized to address the lag outer synchronization for MSCCNN, and the existence of Zeno behavior is ruled out. In addition, two lag outer synchronization criteria for MDCCNN are given on the basis of the node- and edge-based adaptive event-triggered control strategies, and the nonexistence of Zeno behavior is also established. Finally, two examples are provided to demonstrate the feasibility of the proposed control schemes.

Compound-Combination Synchronization for Fractional Hyperchaotic Models with Different Orders

In this paper, we introduce a new type of synchronization for the fractional order (FO) hyperchaotic models with different orders called compound-combination synchronization (CCS). Using the tracking control method, a theorem to calculate the analytical controllers which achieve our proposed synchronization is described and proved. We introduce, also, the FO hyperchaotic complex Lü, Chen, and Lorenz models with complex periodic forcing. The symmetry property is found in the FO hyperchaotic complex Lü, Chen, and Lorenz models. These hyperchaotic models are found in many areas of applied sciences, such as physics and secure communication. These FO hyperchaotic models are used as an example for our proposed synchronization. The numerical simulations show a good agreement with the analytical results. The complexity and existence of additional variables mean that it is safer and interesting to transmit and receive signals in communication theory. The proposed scheme of synchronization is considered a generalization of many types in the literature and other examples can be found in similar studies.

Artificial neural networks: a practical review of applications involving fractional calculus

In this work, a bibliographic analysis on artificial neural networks (ANNs) using fractional calculus (FC) theory has been developed to summarize the main features and applications of the ANNs. ANN is a mathematical modeling tool used in several sciences and engineering fields. FC has been mainly applied on ANNs with three different objectives, such as systems stabilization, systems synchronization, and parameters training, using optimization algorithms. FC and some control strategies have been satisfactorily employed to attain the synchronization and stabilization of ANNs. To show this fact, in this manuscript are summarized, the architecture of the systems, the control strategies, and the fractional derivatives used in each research work, also, the achieved goals are presented. Regarding the parameters training using optimization algorithms issue, in this manuscript, the systems types, the fractional derivatives involved, and the optimization algorithm employed to train the ANN parameters are also presented. In most of the works found in the literature where ANNs and FC are involved, the authors focused on controlling the systems using synchronization and stabilization. Furthermore, recent applications of ANNs with FC in several fields such as medicine, cryptographic, image processing, robotic are reviewed in detail in this manuscript. Works with applications, such as chaos analysis, functions approximation, heat transfer process, periodicity, and dissipativity, also were included. Almost to the end of the paper, several future research topics arising on ANNs involved with FC are recommended to the researchers community. From the bibliographic review, we concluded that the Caputo derivative is the most utilized derivative for solving problems with ANNs because its initial values take the same form as the differential equations of integer-order.

Synchronization of fractional fuzzy cellular neural networks with interactions

In this paper, we introduce fuzzy theory into the fractional cellular neural networks to dynamically enhance the coupling strength and propose a fractional fuzzy neural network model with interactions. Using the Lyapunov principle of fractional differential equations, we design the adaptive control schemes to realize the synchronization and obtain the synchronization criteria. Finally, we provide some numerical examples to show the effectiveness of our obtained results.