4.7 Article

Turing instability and pattern formation of neural networks with reaction-diffusion terms

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Summary: This research investigates the issue of extended dissipative analysis for neural networks with additive time-varying delays. By constructing the augmented Lyapunov-Krasovskii functional and utilizing improved integral inequalities, such as auxiliary function-based integral inequalities, less conservative sufficient conditions are obtained to ensure the asymptotic stability and extended dissipativity of the neural networks. The study aims to solve the H_∞, L_2 - L_∞, passivity, and (Q, S, R)-γ-dissipativity performance problems in a unified framework based on the concept of extended dissipativity. The solvability condition of the designed neural networks with additive time-varying delays is presented in the form of linear matrix inequalities. Finally, the practicality and effectiveness of this approach are demonstrated through four numerical examples.

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