Adaptive synchronization of delayed reaction-diffusion neural networks with unknown non-identical time-varying coupling strengths

Adaptive coupling between neurons widens the entrainment range of the suprachiasmatic nucleus

In many realistic systems, such as neural networks in the brain, the coupling strength between neurons is not fixed, but adaptively adjusts according to their activities. The suprachiasmatic nucleus (SCN), as the main clock in the mammalian brain, has been found to be a plastic neural network, and the coupling strength between neurons is highly dynamical. An important function of the SCN is entrainment, reflecting the ability of the SCN to synchronize with the external light-dark cycle. The entrainment ability is reflected by the entrainment range, which is a period range for the external light-dark cycle to which the SCN can entrain. In this article, we investigated whether the entrainment range of the SCN is affected by the adaptive coupling. We use a modified Kuramoto model with external light-dark cycle. We found that when the light sensitivity is larger than the fixed coupling strength (the coupling strength without adaptive rules), adaptive coupling can widen the entrainment range. Our findings help to understand the impact of the adaptive coupling between oscillatorty neurons on the collective behavior of the SCN, and provides a possible explanation for the plasticity of coupling in the master clock network.

Distributed Adaptive Tracking Synchronization for Coupled Reaction-Diffusion Neural Network

This paper considers the tracking synchronization problem for a class of coupled reaction-diffusion neural networks (CRDNNs) with undirected topology. For the case where the tracking trajectory has identical individual dynamic as that of the network nodes, the edge-based and vertex-based adaptive strategies on coupling strengths as well as adaptive controllers, which demand merely the local neighbor information, are proposed to synchronize the CRDNNs to the tracking trajectory. To reduce the control costs, an adaptive pinning control technique is employed. For the case where the tracking trajectory has different individual dynamic from that of the network nodes, the vertex-based adaptive strategy is proposed to drive the synchronization error to a relatively small area, which is adjustable according to the parameters of the adaptive strategy. This kind of adaptive design can enhance the robustness of the network against the external disturbance posed on the tracking trajectory. The obtained theoretical results are verified by two representative examples.