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Zhusubaliev Z. T., Emelyanova E. Y. On synchronization of quasi-periodic oscillation at C-bifurcations in a piecewise-linear nonautonomous dynamic system. Izvestiya VUZ. Applied Nonlinear Dynamics, 2000, vol. 8, iss. 5, pp. 57-71. DOI: 10.18500/0869-6632-2000-8-5-57-71
On synchronization of quasi-periodic oscillation at C-bifurcations in a piecewise-linear nonautonomous dynamic system
The behaviour is examined of a piecewise—linear dynamic system with external periodic force at C-bifurcations which is related to resonance cycles arising from synchronization of quasi—periodic oscillation. As example the dynamics of the system of automatic control with pulse-width modulation first kind is considered which is represented by а three—dimensional piecewise—linear nonautonomous dynamic system. It has been revealed that within the parameter plane there are domains of existence of resonance cycles on two—dimension thorus (domains of synchronization). These domains have specific shape similar to Arnold’s tongues, but differ from them essentially in their internal structural organization and bifurcation transitions which cannot be achieved in smooth dynamic systems in principle. A detailed analytical description of C—boundaries structure and bifurcation transitions within the synchronization domain is there in this paper.
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