For citation:
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
Autooscillating system with compensated dissipation: dynamics of approximated discrete map
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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