Chaos and hyperchaos via secondary Neimark–Sacker bifurcation in a model of radiophysical generator
- 145 Downloads
Using an example of a radiophysical generator model, scenarios for the formation of various chaotic attractors are described, including chaos and hyperchaos. It is shown that as a result of a secondary Neimark–Sacker bifurcation, a hyperchaos with two positive Lyapunov exponents can occur in the system. A comparative analysis of chaotic attractors born as a result of loss of smoothness of an invariant curve, as a result of period-doubling bifurcations, and as a result of secondary Neimark–Sacker bifurcation was carried out.
KeywordsHyperchaos Secondary Neimark–Sacker bifurcation Quasiperiodic oscillations Multistability Lyapunov exponents
Mathematics Subject Classification37C55 37E45 37E99
Authors thank Igor Sataev, Alexey Kazakov and Serhiy Yanchuk for fruitful discussion of this problem.
The work was carried out with the financial support of the Russian Foundation of Basic Research, Grant No. 18-32-00285 (Introduction, Sects. 2, 3, 4.1) and Russian Science Foundation, Grant No. 17-12-01008 (Sect. 4.2). Analysis of multistability was carried out in the frame of project of the Russian Foundation of Basic Research, Grant No. 19-02-00610.
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
- 25.Gonchenko, A.S., Gonchenko, S.V., Shilnikov, L.P.: Towards scenarios of chaos appearance in three-dimensional maps. Russ. J. Nonlinear Dyn. 8, 3–28 (2012). (Russian)Google Scholar
- 30.Amabili, M., Karagiozis, K., Païdoussis, M.P.: Hyperchaotic behaviour of shells subjected to flow and external force. In: ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels, American Society of Mechanical Engineers, pp. 1209–1217 (2010)Google Scholar
- 35.Kuznetsov, A.P., Stankevich, N.V.: Autonomous systems with quasiperiodic dynamics. Examples and their properties: review. Izv. VUZ Appl. Nonlinear Dyn. 23, 71–93 (2015). (in Russia)Google Scholar