Chan, Whei-Ching C.; Shi, Shaoyun Heteroclinic orbits arising from coupled Chua’s circuits. (English) Zbl 1082.34036 Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, No. 3, 571-582 (2003). This paper proves existence of traveling waves for a system of partial differential equations modelling cellular neural networks (traveling waves were already observed numerically). The problem is reduced to look for heteroclinic orbits of a system of three ordinary differential equations depending parametrically on the speed of the wave. Using a singular perturbation type approach, heteroclinic orbits are rigourously proved for large values of the speed. Reviewer: Massimiliano Berti (Trieste) Cited in 1 Document MSC: 34C37 Homoclinic and heteroclinic solutions to ordinary differential equations Keywords:heteroclinic orbits; traveling wave solution PDFBibTeX XMLCite \textit{W.-C. C. Chan} and \textit{S. Shi}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, No. 3, 571--582 (2003; Zbl 1082.34036) Full Text: DOI References: [1] DOI: 10.1142/S0218127492000379 · Zbl 0875.94132 · doi:10.1142/S0218127492000379 [2] DOI: 10.1142/S021812749200080X · Zbl 0876.34061 · doi:10.1142/S021812749200080X [3] Bernfeld S. R., An Introduction to Nonlinear Boundary Value Problems (1974) · Zbl 0286.34018 [4] DOI: 10.1006/jdeq.1998.3478 · Zbl 0911.34050 · doi:10.1006/jdeq.1998.3478 [5] Chua L. O., Archiv für Elektronik und Ubertragungstechnik 46 pp 250– [6] DOI: 10.1142/9789812798589 · doi:10.1142/9789812798589 [7] C. De Coster and P. Habets, Nonlinear Analysis and BVP for ODE 371, ed. F. Zanolin (Springer Wien, NY, 1996) pp. 1–78. · Zbl 0889.34018 [8] DOI: 10.1016/S0378-4371(98)00389-6 · doi:10.1016/S0378-4371(98)00389-6 [9] Kennedy M., Frequenz 46 pp 66– [10] DOI: 10.1142/9789812798855_0003 · doi:10.1142/9789812798855_0003 [11] DOI: 10.1142/S0218127492000380 · Zbl 0875.94136 · doi:10.1142/S0218127492000380 [12] DOI: 10.1142/9789812798855_0015 · doi:10.1142/9789812798855_0015 [13] DOI: 10.1002/cta.4490130109 · doi:10.1002/cta.4490130109 [14] Zhong G. H., IEEE Trans. Circuits Syst. 32 pp 501– · doi:10.1109/TCS.1985.1085728 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.