Adaptive Synchronization of Fractional-Order Complex-Valued Neural Networks With Time-Varying Delays

In this paper, the adaptive synchronization of fractional-order complex-valued neural networks with time-varying delays (FOCVNNTDs) is investigated. First, two novel fractional-order differential inequalities with time delays are established, which can be seen as an extension of Halanay inequality. Besides, complete synchronization and quasi-projective synchronization of FOCVNNTDs are investigated based on the two novel inequalities using a novel adaptive controller. In addition, instead of separating the complex-valued neural networks into two real-valued networks, a non-decomposition method is adopted to study the adaptive synchronization of FOCVNNTDs, which avoids the difficulty and complexity of theoretical analysis. Finally, some numerical simulation examples are provided to demonstrate the validity of our theory.

Automated summary

This paper investigates the adaptive synchronization of fractional-order complex-valued neural networks with time-varying delays (FOCVNNTDs). Two novel fractional-order differential inequalities with time delays are established, which extend the Halanay inequality. By using a novel adaptive controller based on these inequalities, the complete synchronization and quasi-projective synchronization of FOCVNNTDs are achieved. A non-decomposition method is adopted to study the adaptive synchronization of FOCVNNTDs, which avoids the complexity of theoretical analysis.