Funct. Mater. 2013; 20 (2): 227-233.
Influence of nonlinear dissipation and external perturbations on transition scenarios to the chaos in the Lorenz-Haken system
Sumy State University, 2 Rimskiy-Korsakov Str., 40000 Sumy, Ukraine
We studied an influence of nonlinear dissipation and external perturbations on transition scenarios to the chaos in the Lorenz-Haken system. It was shown that variation in the values of external potential parameters leads to parameters domain formation which results in the chaos appearance. We have found that in the modified Lorenz-Haken system transitions from the regular to chaotic dynamics can be of Ruelle-Takens scenario, Feigenbaum scenario, or through intermittency.
1. J.N.Blakely, L.Illing, D.J.Gauthier, IEEE J. of Quant. Electron., 40, 299 (2004). http://dx.doi.org/10.1109/JQE.2003.823021
2. G.D.Van Wiggeren, R.Roy, Phys. Rev. Lett., 88, 097903 (2002). http://dx.doi.org/10.1103/PhysRevLett.88.097903
3. R.Meucci, M.Ciofini, R.Abbate, Phys. Rev. E, 53, R5537 (1996). http://dx.doi.org/10.1103/PhysRevE.53.R5537
4. C.Bracikowski, R.Roy, Chaos, 1, 49 (1991). http://dx.doi.org/10.1063/1.165817
5. Z.Gills, C.Iwata, R.Roy, Phys. Rev. Lett., 69, 3169 (1992). http://dx.doi.org/10.1103/PhysRevLett.69.3169
6. S.Boccaleti et al., Phys. Rep., 392, 103 (2000). http://dx.doi.org/10.1016/S0370-1573(99)00096-4
7. H.Haken, Synergetics, Springer, New York (1983). http://dx.doi.org/10.1007/978-3-642-88338-5
8. A.I.Olemskoi, Theory of Structure Transformations in Non-equilibrium Condensed Matter, Nova Science Publishers Inc., New York (1999).
9. D.O.Kharchenko, I.A.Knyaz′, Eur. Phys. J. B, 32, 375 (2003); http://dx.doi.org/10.1140/epjb/e2003-00112-9
D.O.Kharchenko, I.A.Knyaz′, J. Phys. Stud., 8, 299 (2004);
D.O.Kharchenko, I.A.Knyaz, Proc. of SPIE, 5507, 7 (2004).
10. A.I.Olemskoi, A.V.Khomenko, Zh. Eksper. i Teor. Phys., 110, 2144 (1996).
11. V.O.Kharchenko, J. Phys. Stud., 12, 2001 (2008).
12. T.Poston, I.N.Stewart, Catastrophe Theory and its Applications, Pitman, London (1978).
13. E.D.Belokolos, V.O.Kharchenko, D.O.Kharchenko, Chaos, Solitons and Fractals, 41, 2595 (2009). http://dx.doi.org/10.1016/j.chaos.2008.09.049
14. G.Benettin, Meccanica, 15, 9 (1980). http://dx.doi.org/10.1007/BF02128236
15. H.G.Shuster. Deterministic Chaos, An Introduction, Physik-Verlag, Weinheim (1984).
16. R.Z.Sagdeev, D.A.Usikov, G.M.Zaslavskii, Nonlinear Physics: from the Pendulum to Turbulence and Chaos, Harwood Academic, Chur (1988).
17. J.C.Sprott, Chaos Time-Series Analysis, Oxford University Press, Oxford (2003).
18. E.D.Belokolos, V.O.Kharchenko, Functional Materials, 15, 496 (2008).