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• W3048809611 abstract "This chapter is concerned with the problems of positivity and stability of nonlinear time-delay systems in the area of neural networks. The concept of positivity is first developed and characterized for various models of neural networks with delays including Hopfield neural networks, bidirectional associative memory neural networks and inertial neural networks. It will be shown by utilizing the property of order-preserving of neuron activation functions that for nonnegative connection weights of neurons, state trajectories of the networks initializing from a positive cone called the admissible set of initial conditions are always nonnegative subject to nonnegative inputs. Then, the exponential stability of positive equilibriums of the underlying models is investigated by a systematic approach involving extended comparison techniques via differential and integral inequalities. Unified conditions for the existence and exponential stability of positive equilibriums are derived in the form of linear programming (LP) conditions with M-matrix, which can be effectively solved by various convex algorithms. Numerical examples and simulations are provided to demonstrate the applicability and effectiveness of the derived theoretical results." @default.
• W3048809611 created "2020-08-18" @default.
• W3048809611 creator A5064063674 @default.
• W3048809611 date "2020-08-11" @default.
• W3048809611 modified "2023-10-16" @default.
• W3048809611 title "Positivity and Stability of Nonlinear Time-Delay Systems in Neural Networks" @default.
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• W3048809611 doi "https://doi.org/10.1007/978-3-030-49123-9_15" @default.
• W3048809611 hasPublicationYear "2020" @default.
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