ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Kuznetsov A. P., Kuznetsov S. P., Savin A. V., Savin D. V. Autooscillating system with compensated dissipation: dynamics of approximated discrete map. Izvestiya VUZ. Applied Nonlinear Dynamics, 2008, vol. 16, iss. 5, pp. 127-138. DOI: 10.18500/0869-6632-2008-16-5-127-138

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Autooscillating system with compensated dissipation: dynamics of approximated discrete map

Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Kuznetsov Sergey Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Savin Aleksej Vladimirovich, Saratov State University
Savin Dmitrij Vladimirovich, Saratov State University

The pulse-driven van der Pol oscillator with the external pulse amplitude depending on the system variables is considered. The discrete map for values of the system variables just before the pulse moment was obtained by the slow-varying-amplitude method. Further the parameter space of this map was analyzed, and the existence of the Hamiltonian critical behavior in this system was shown. The remarkable fact is that our system is the system with the dissipation depending not only on the parameter values, but on the variable values too. Also the existence of the quasi-periodicity and the synchronization near the unstable cycle was shown.

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