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In this paper, synchronization of an inertial neural network with time-varying delays is investigated. Based on the variable transformation method, we transform the second-order differential equations into the first-order differential equations. Then, using suitable Lyapunov-Krasovskii functionals and Jensen's inequality, the synchronization criteria are established in terms of linear matrix inequalities. Moreover, a feedback controller is designed to attain synchronization between the master and slave models, and to ensure that the error model is globally asymptotically stable. Numerical examples and simulations are presented to indicate the effectiveness of the proposed method. Besides that, an image encryption algorithm is proposed based on the piecewise linear chaotic map and the chaotic inertial neural network. The chaotic signals obtained from the inertial neural network are utilized for the encryption process. Statistical analyses are provided to evaluate the effectiveness of the proposed encryption algorithm. The results ascertain that the proposed encryption algorithm is efficient and reliable for secure communication applications.

This paper deals with the problem of existence and uniform stability analysis of fractional-order complex-valued neural networks with constant time delays. Complex-valued recurrent neural networks is an extension of real-valued recurrent neural networks that includes complex-valued states, connection weights, or activation functions. This paper explains sufficient condition for the existence and uniform stability analysis of such networks. Three numerical simulations are delineated to substantiate the effectiveness of the theoretical results.

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