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This paper probes deep into the synchronization control of high-order inertial Hopfield neural network with time delay, considering both inertia term and high-order term. Specifically, a second-order differential system was transformed into a first-order differential system, through proper variable substitution. Then, the sufficient conditions for exponential synchronization of the response system were theorized, with the aid of the fundamental solution matrix of the differential equation. The theoretical conditions were verified through an example analysis. The research findings have great application potential in production, communication, and automation.

Synchronization Control of High-Order Inertial Hopfield Neural Network with Time Delay