Related Experiment Video
Updated: Apr 12, 2026

Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond
Published on: June 24, 2015
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.
Related Concept Videos
Neural Circuits
Neuronal pools are collections of nerve cells with similar functions and interact through chemical and electrical signals. These pools include both interneurons (the central neural circuit nodes that...
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
Reaction Mechanisms: Rate-limiting Step Approximation
Propagation of Action Potentials
Neurons (nerve cells) have a resting membrane potential, with a slightly negative charge inside compared to outside. This is maintained by ion channels, such as sodium (Na+) and potassium (K+) channels, which control the flow of ions. When a stimulus, like a touch or a signal from another neuron, triggers the neuron, sodium channels open, allowing sodium ions to...
Open and closed-loop control systems
An open-loop control system operates without feedback from the output. It consists of two primary elements: the controller and the controlled process. The controller receives an input signal...
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....

