Mean-square exponential input-to-state stability of stochastic fuzzy delayed Cohen-Grossberg neural networks
Wentao Wang
Abstract
We consider a class of stochastic fuzzy delayed Cohen-Grossberg neural networks without global Lipschitz condition. Based on local Lipschitz condition, we prove the solutions of the given neural networks exist globally and are mean-square exponentially input-to-state stable. Moreover, we highlight the advantages of our novel results by comparing with the results in Zhu and Li (2012 Li, B., & Xu, D. (2012). Existence and exponential stability of periodic solution for impulsive Cohen–Grossberg neural networks with time-varying delays. Applied Mathematics and Computation, 219(5), 2506–2520. https://doi.org/10.1016/j.amc.2012.08.086[Crossref], [Web of Science ®] , [Google Scholar]) as well as a numerical example.
Topics & Concepts
Lipschitz continuityArtificial neural networkExponential stabilityComputer scienceStability (learning theory)ComputationApplied mathematicsState (computer science)Exponential functionSquare (algebra)Stochastic neural networkFuzzy logicMean squareClass (philosophy)Control theory (sociology)MathematicsAlgorithmArtificial intelligenceRecurrent neural networkPure mathematicsMathematical analysisNonlinear systemMachine learningPhysicsControl (management)GeometryQuantum mechanicsNeural Networks Stability and SynchronizationAdvanced Memory and Neural Computingstochastic dynamics and bifurcation