Maistrenko, Yu. L.; Maistrenko, V. L.; Vikul, S. I.; Chua, L. O. Bifurcations of attracting cycles from time-delayed Chua’s circuit. (English) Zbl 0885.58059 Int. J. Bifurcation Chaos Appl. Sci. Eng. 5, No. 3, 653-671 (1995). Summary: We study the bifurcations of attracting cycles for a three-segment (bimodal) piecewise-linear continuous one-dimensional map. Exact formulas for the regions of periodicity of any rational rotation number (Arnold’s tongues) are obtained in the associated three-dimensional parameter space. It is shown that the destruction of any Arnold’s tongue is a result of a border-collision bifurcation, and is followed by the appearance of a cycle of intervals with the same rotation number, whose dynamics is determined by a skew tent map. Finally, for the interval cycle the merging bifurcation corresponds to a homoclinic bifurcation of some point cycle. Cited in 45 Documents MSC: 37G99 Local and nonlocal bifurcation theory for dynamical systems 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 37C70 Attractors and repellers of smooth dynamical systems and their topological structure 94C99 Circuits, networks Keywords:bifurcations; attracting cycles; one-dimensional map; rotation number; Arnold’s tongue PDFBibTeX XMLCite \textit{Yu. L. Maistrenko} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 5, No. 3, 653--671 (1995; Zbl 0885.58059) Full Text: DOI