Adaptive synchronization of stochastic complex dynamical networks and its application

Abstract

This paper investigates exponential synchronization for stochastic complex dynamical networks with reaction-diffusion terms and S-type distributed delays. Based on a generalized Halanay inequality and Poincaré inequality, adaptive control strategies for exponential synchronization are established by constructing a simple Lyapunov-Krasovskii functional candidate and utilizing the truncation method. Some numerical examples are provided to demonstrate the effectiveness of the obtained results. Finally, the proposed adaptive synchronization theoretical results are successfully applied to image encryption.

Stability of stochastic impulsive reaction–diffusion neural networks with S-type distributed delays and its application to image encryption

“…Therefore, for a class of infinite delayed system, we can impose conditions on the delay term toward stability after the limitation of the infinitesimal. Moreover, the obtained results generalise Halanay inequality [8], inequalities with infinite delay [31,37], and other impulsive inequalities with finite delay [15,39,42] to be suitable for infinite delayed impulsive system. Lemma 7.…”

“…From Tables 3 and 4, the entropy 7.9993 of Lena is close to 8 and the correlations of two adjacent pixels agree with the description of Figure 7, which also imply the random-like appearance of the ciphered images. [4,27,37], the proposed scheme is more robust to statistic attacks because the absolute average correlation of two adjacent pixels for Lady and Pepper is 2.63e-3 which is smaller than 3.35e-3 of [37] and 3.40e-3 of [27] and the correlation for Lena is smaller than 9.20e-3 of [4]. Besides, the proposed scheme is robust to differential attack because NPCR reaches 0.99 and UACI reaches 0.33.…”

“…Remark 1. When γ = 1, the impulsive Halanay-type inequality degenerates to an inequality without impulse which has been studied in [37] under the stability condition a + b < 0. Therefore, it is straightforward to deduce the following result.…”

“…In [31], an S-type distributed delay in terms of Lebesgue-Stieltjes integration, which includes both of the above delays, was incorporated over an infinitely long duration and had better description of hysteresis phenomenon in networks. Since then, the stability analysis of neural networks with S-type distributed delays has also attracted considerable interest [31,37]. Recently, there are also some significant works about probabilistic delays and model-dependent time delays [3,32].…”

“…More development about the application of delayed neural networks to image encryption refers to [4,14,27] and references therein. As mentioned above, SIRDNNs with S-type distributed delays can model real world systems well, and the S-type distributed delays sometimes generate chaotic phenomenon which benefits the encryption process of image encryption [37]. However, there is relatively less work about the stability and application of SIRDNNs with S-type distributed delays because the effect of the delay defined on (−∞, t 0 ] is difficult to be eliminated and its non-differentiability blocks the way of constructing Lyapunov-Krasovskii functional with distributed term.…”