Polytechnicheskaya 77, Saratov, 410054, Russia
Saratov State Technical University
Kuznetsov A. P., Kuznetsov S. P., Pozdnyakov M. V., Sedova Y. V.
Universal two-dimensional map and its radiophysical realization
2012, Vol. 8, No. 3, pp. 461-471
We suggest a simple two-dimensional map, parameters of which are the trace and Jacobian of the perturbation matrix of the fixed point. On the parameters plane it demonstrates the main universal bifurcation scenarios: the threshold to chaos via period-doublings, the situation of quasiperiodic oscillations and Arnold tongues. We demonstrate the possibility of implementation of such map in radiophysical device.
Kuznetsov A. P., Pozdnyakov M. V., Sedova Y. V.
Coupled universal maps demonstrating Neimark–Saker bifurcation
2012, Vol. 8, No. 3, pp. 473-482
We examine the dynamics of the coupled system consisting of subsystems, demonstrating the Neimark–Sacker bifurcation. The study of coupled maps on the plane of the parameters responsible for such bifurcation in the individual subsystems is realized. On the plane of parameters characterizing the rotation numbers of the individual subsystems we reveal the complex structures consisting of the quasi-periodic modes of different dimensions and the exact periodic resonances of different orders.