Li, Yongkun; Zhu, Lifei; Liu, Ping Existence and stability of periodic solutions of delayed cellular neural networks. (English) Zbl 1086.92002 Nonlinear Anal., Real World Appl. 7, No. 2, 225-234 (2006). Summary: We use the continuation theorem of coincidence degree theory [see R. E. Gaines and J. L. Mawhin, Coincidence degree, and nonlinear differential equations. (1977; Zbl 0339.47031); J. L. Mawhin, Topological degree methods in nonlinear boundary value problems. (1979; Zbl 0414.34025)] and Lyapunov functions to study the existence and stability of positive periodic solutions for cellular neural networks (CNNs) with distributed delays \[ dx_i/dt=-b_i(t)x_i(t)+ \sum^n_{j=1}a_{ij}(t)f_j(x_j(t))+ \sum^n_{j=1}b_{ij}(t)f_j(x_j (\zeta_{ij}(t,x_j(t)))) +I_i(t), \] and cellular neural networks (CNNs) with state-dependent delays \[ dx_i/dt=-b_i(t)x_i(t)+ \sum^n_{j=1}a_{ij}(t)f_j(x_j(t))+ \sum^n_{j=1}b_{ij}(t)f_j\left(\int^\infty_0 k_{ij}(u)x_j(t-u)\,du\right)+I_i(t), \] \(i,j=1,2\dots,n\). Cited in 14 Documents MSC: 92B20 Neural networks for/in biological studies, artificial life and related topics 34K13 Periodic solutions to functional-differential equations 68T05 Learning and adaptive systems in artificial intelligence 34K20 Stability theory of functional-differential equations Keywords:state-dependent delay; periodic solutions; stability Citations:Zbl 0339.47031; Zbl 0414.34025 PDFBibTeX XMLCite \textit{Y. Li} et al., Nonlinear Anal., Real World Appl. 7, No. 2, 225--234 (2006; Zbl 1086.92002) Full Text: DOI References: [1] Cao, J., New results concerning exponential stability and periodic solutions of delayed cellular neural networks, Phys. Lett. A, 307, 136-147 (2003) · Zbl 1006.68107 [2] Chua, L. O., CNNA Paradigm for Complexity (1998), World Scientific: World Scientific Singapore [3] Chua, L. O.; Yang, L., Cellular Neural networks: applications, IEEE Trans. Circuits Syst. I, 35, 1273-1290 (1988) [4] Gaines, R. E.; Mawhin, J. L., Coincidence degree and Nonlinear Differential Equations (1977), Springer: Springer Berlin · Zbl 0339.47031 [5] Li, Y. K.; Kuang, Y., Periodic solutions of periodic delay Lotka-Volterra equations and systems, J. Math. Anal. Appl., 255, 260-280 (2001) · Zbl 1024.34062 [6] J.L. Mawhin, Topological degree methods in nonlinear boundary value problems, CBMS Regional Conference Series in Mathematics, No. 40, American Mathematical Society, Providence, RI, 1979.; J.L. Mawhin, Topological degree methods in nonlinear boundary value problems, CBMS Regional Conference Series in Mathematics, No. 40, American Mathematical Society, Providence, RI, 1979. · Zbl 0414.34025 [7] Roska, T.; Vandewalle, J., Cellular Neural Networks (1995), Wiley: Wiley New York This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.