Nonlinear Dynamics

, Volume 97, Issue 4, pp 2355–2370 | Cite as

Chaos and hyperchaos via secondary Neimark–Sacker bifurcation in a model of radiophysical generator

  • Nataliya StankevichEmail author
  • Alexander Kuznetsov
  • Elena Popova
  • Evgeniy Seleznev
Original paper


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.


Hyperchaos Secondary Neimark–Sacker bifurcation Quasiperiodic oscillations Multistability Lyapunov exponents 

Mathematics Subject Classification

37C55 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. 234.1) 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.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Radio-Electronics and TelecommunicationYuri Gagarin State Technical University of SaratovSaratovRussia
  2. 2.Saratov BranchKotel’nikov’s Institute of Radio-Engineering and Electronics of RASSaratovRussia
  3. 3.Department of Applied CyberneticsSaint-Petersburg State UniversitySaint-PetersburgRussia

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