Pinning Control Strategies for Synchronization of Linearly Coupled Neural Networks With Reaction–Diffusion Terms

Abstract

Two types of coupled neural networks with reaction-diffusion terms are considered in this paper. In the first one, the nodes are coupled through their states. In the second one, the nodes are coupled through the spatial diffusion terms. For the former, utilizing Lyapunov functional method and pinning control technique, we obtain some sufficient conditions to guarantee that network can realize synchronization. In addition, considering that the theoretical coupling strength required for synchronization may be much larger than the needed value, we propose an adaptive strategy to adjust the coupling strength for achieving a suitable value. For the latter, we establish a criterion for synchronization using the designed pinning controllers. It is found that the coupled reaction-diffusion neural networks with state coupling under the given linear feedback pinning controllers can realize synchronization when the coupling strength is very large, which is contrary to the coupled reaction-diffusion neural networks with spatial diffusion coupling. Moreover, a general criterion for ensuring network synchronization is derived by pinning a small fraction of nodes with adaptive feedback controllers. Finally, two examples with numerical simulations are provided to demonstrate the effectiveness of the theoretical results.

Passivity analysis of impulsive coupled reaction-diffusion neural networks with and without time-varying delay

“…The initial value and boundary value conditions associated with network (25) where Φ i ðx; tÞði ¼ 1; 2; …; NÞ is a bounded and continuous function on Ω Â ½Àτ; 0. Define e i ðx; tÞ ¼ ðe i1 ðx; tÞ; e i2 ðx; tÞ; …; e in ðx; tÞÞ T ¼ z i ðx; tÞÀw n ; i ¼ 1; 2; …; N (w n denotes the same meanings as this in Section 3).…”

“…Practically, the diffusion phenomena could not be ignored in neural networks and electric circuits once electrons transport in a nonuniform electromagnetic field [18,19]. Thus, it is important and interesting to study the coupled reaction-diffusion neural networks (CRDNNs) [20][21][22][23][24][25]. Liu [20] studied the μ-synchronization and pinning control problems for a class of CRDNNs with Dirichlet boundary conditions and unbounded time-delays.…”

Synchronization in nonlinear complex networks with multiple time‐varying delays via adaptive aperiodically intermittent control

“…[15][16][17] In most of the existing works on synchronization of complex networks, one assumption adopted is that the inner couplings are linear such as the references [18][19][20] and linear coupling considers the state variables as a priori knowledge. [15][16][17] In most of the existing works on synchronization of complex networks, one assumption adopted is that the inner couplings are linear such as the references [18][19][20] and linear coupling considers the state variables as a priori knowledge.…”

Stability and synchronization analysis of inertial memristive neural networks with time delays

“…The global exponential synchronization of coupled neural networks with stochastic perturbations and mixed time-varying delays has been discussed in Wang et al (2015) and synchronization criteria have been derived based on multiple Lyapunov theory. Two types of coupled neural networks with reaction-diffusion terms have been considered in Wang et al (2016) and the general criterion for ensuring network synchronization has been derived by pinning a small fraction of nodes with adaptive feedback controllers. A sufficient condition for the exponential synchronization of fractional-order complex networks via pinning impulsive control has been derived using Lyapunov function and Mittag-Leffler function in Wang et al (2015).…”