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Journal of Applied Nonlinear Dynamics 5(2) (2016) 161--167 | DOI:10.5890/JAND.2016.06.003

A.P. Kuznetsov; Yu.V. Sedova

Kotel’nikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelenaya 38, Saratov, 410019, Russian Federation

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Abstract

A model with hyperchaos is studied by means of Lyapunov twoparameter analysis. The regions of chaos and hyperchaos, as well as autonomous quasiperiodicity are identified. We discuss the picture of domains of different regimes in the parameter plane of coupled systems, corresponding to the cases of interaction of quasiperiodic and hyperchaotic subsystems.

References

1. [1]	Rossler, O.E. (1979), An equation for hyperchaos, Physics Letters A, 71, 155-157.

2. [2]	Klein M., Baier G. and Rössler, O.E. (1991), From N-tori to hyperchaos, Chaos, Solitons & Fractals, 1 105-118.

3. [3]	Barreto E., Hant B.R., Grebogi C. and Yorke, J.A. (1997), From high dimensional chaos to stable periodic orbits: The structure of parameter space, Physical Review Letters, 78, 4561-4564.

4. [4]	Harrison, M.A. and Lai,Y.-C. (1999), Route to high-dimensional chaos, Physical Review E, 59, 3799-3802.

5. [5]	Kapitaniak, T., Maistrenko, Yu. and Popovych, S. (2000), Chaos-hyperchaos transition, Physical Review E, 62, 1972-1976.

6. [6]	Richter, H. (2002), The generalized Hénon maps: examples for higher-dimensional chaos, International Journal of Bifurcation and Chaos, 12, 1371-1384.

7. [7]	Chen, Z., Yang, Y., Qi, G. and Yuan, Z. (2007), A novel hyperchaos system only with one equilibrium, Physics Letters A, 360, 696-701.

8. [8]	Harikrishnan, K.P., Misra, R. and Ambika, G. (2013), On the transition to hyperchaos and the structure of hyperchaotic attractors, The European Physical Journal B, 86, 1-12.

9. [9]	Han, X., Jiang, B. and Bi, Q. (2010) 3-torus, quasi-periodic bursting, symmetric subHopf/fold-cycle bursting, subHopf/fold-cycle bursting and their relation, Nonlinear Dynamics, 61 667-676.

10. [10]	Wei, Z. and Zhang, W. (2014), Hidden hyperchaotic attractors in a modified Lorenz-Stenflo system with only one stable equilibrium, International Journal of Bifurcation and Chaos, 24 , 1450127.

11. [11]	Pikovsky, A., Rosenblum, M. and Kurths, J. (2001), Synchronization. A Universal Concept in Nonlinear Sciences, Cambridge University Press.

12. [12]	Kuznetsov, A.P., Kuznetsov, S.P. and Stankevich, N.V. (2010) A simple autonomous quasiperiodic selfoscillator, Communications in Nonlinear Science and Numerical Simulation, 15, 1676-1681.

13. [13]	Anishchenko, V., Nikolaev, S. and Kurths, J. (2007), Peculiarities of synchronization of a resonant limit cycle on a two-dimensional torus, Physical Review E, 76, 046216.

14. [14]	Baesens, C., Guckenheimer, J., Kim, S. and MacKay, R.S. (1991) Three coupled oscillators: mode locking, global bifurcations and toroidal chaos, Physica D: Nonlinear Phenomena 49 387-475.

15. [15]	Emelianova, Yu.P., Kuznetsov, A.P., Sataev, I.R. and Turukina, L.V.(2013) Synchronization and multi frequency oscillations in the low-dimensional chain of the self-oscillators, Physica D: Nonlinear Phenomena, 244, 36-49.

16. [16]	Emelianova, Y.P., Kuznetsov, A.P., Turukina, L.V., Sataev, I.R. and Chernyshov, N.Yu. (2014) A structure of the oscillation frequencies parameter space for the system of dissipatively coupled oscillators, Communications in Nonlinear Science and Numerical Simulation, 19, 1203-1212.