Jiang, Fangfang; Shen, Jianhua; Li, Xiaodi The LMI method for stationary oscillation of interval neural networks with three neuron activations under impulsive effects. (English) Zbl 1263.92003 Nonlinear Anal., Real World Appl. 14, No. 3, 1404-1416 (2013). Summary: We investigate the stationary oscillations of interval neural networks with three neuron activation functions and time-varying delays under impulsive perturbations. Several theorems are given which present some sufficient conditions to guarantee the existence, uniqueness, and global exponential stability of periodic solutions (i.e., stationary oscillation) based on a Lyapunov functionals approach and inequality analysis techniques. The obtained results can be easily checked by the linear matrix inequality control toolbox in MATLAB. Finally, an example is given to illustrate the advantage of the obtained results. Cited in 5 Documents MSC: 92B20 Neural networks for/in biological studies, artificial life and related topics 34K13 Periodic solutions to functional-differential equations 34K45 Functional-differential equations with impulses 15A45 Miscellaneous inequalities involving matrices 34K20 Stability theory of functional-differential equations 92-04 Software, source code, etc. for problems pertaining to biology Keywords:impulsive delay differential inequality; linear matrix inequalities; LMIs; Lyapunov functionals Software:LMI toolbox; Matlab PDFBibTeX XMLCite \textit{F. Jiang} et al., Nonlinear Anal., Real World Appl. 14, No. 3, 1404--1416 (2013; Zbl 1263.92003) Full Text: DOI