Mean square H<inf>&#x2212;</inf> synchronization of coupled nonlinear delay stochastic partial differential systems

Abstract

This paper considers the synchronization problem for the coupled nonlinear delay stochastic partial differential systems(SPDSs), both mean square asymptotical synchronization and mean square H∞ synchronization are studied. Making use of the Lyapunov-Krasoviskii functional method and Itö formula, sufficient conditions are derived which guarantee the mean square asymptotical synchronization of the coupled nonlinear delay SPDSs. When the external disturbances appear in the coupled nonlinear delay SPDSs, the mean square H∞ synchronization is dealt with and sufficient criterion is provided. Finally, numerical examples are given to illustrate the correctness of our results.

synchronization of coupled reaction‐diffusion neural networks with mixed delays

“…The distributed time-delay network would have a great influence on the synchronization analysis. Therefore, the model presented in this article generalizes the corresponding models of recent works [11,[13][14][15][16][23][24][25][26]. We will use the Lyapunov-Krasoviskii functional V(t) (9) to treat the infinite distributed delay in the complex network (3).…”

“…The synchronization problem of linearly coupled neural networks with reaction-diffusion terms is investigated by the adaptive strategies [14,16,26]. Based on the Lyapunov-Krasoviskii functional method and It€ o formula, the mean square asymptotical synchronization and mean square H 1 synchronization problems for the coupled nonlinear delay stochastic partial differential systems are studied [23]. The exponential synchronization problem for a class of complex spatio-temporal networks with spacevarying coefficients is addressed to design distributed proportional-spatial derivative (P-sD) state feedback controllers [24].…”

“…It is worth noting that, in many current and pre-existed results about coupled reaction-diffusion neural networks, some papers don't consider discrete time-delays [11,[14][15][16][24][25][26], or only consider the constant delay [23]. Furthermore, this hypothesis is widely used in many preexisted results about coupled time-delays of coupled reaction-diffusion neural networks [13,14,16,25].…”

“…Synchronization is particularly pronounced in complex networks for PDEs. Consensus techniques for coupled semilinear diffusion PDEs, focused on revealing and exploiting this synchronization, have been under development since 2010 [11], but have been limited to discrete time-delay [23] or without delay [24], however, there is still no a breakthrough about mixed delays (that is, discrete and infinite distributed delay). The objective of this article is to derive simple conditions for the exponential synchronization for coupled reaction-diffusion neural networks with mixed delays and Dirichlet boundary condition.…”