ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Kuznetsov A. P., Savin A. V., Savin D. V. Conservative and dissipative dynamics of Ikeda map. Izvestiya VUZ. Applied Nonlinear Dynamics, 2006, vol. 14, iss. 2, pp. 94-106. DOI: 10.18500/0869-6632-2006-14-2-94-106

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text:
(downloads: 177)
Article type: 

Conservative and dissipative dynamics of Ikeda map

Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Savin Aleksej Vladimirovich, Saratov State University
Savin Dmitrij Vladimirovich, Saratov State University

Different methods for investigation of dissipative, nearly conservative and conservative systems have been demonstrated on the example of Ikeda map. The method for two-parameter analysis of dynamics of conservative systems has been proposed. Significant changes in the structure of the parameter and phase space of Ikeda map when dissipation decreases have been revealed. Tasks for seminars and computer practices have been proposed.

Key words: 
  1. Feudel U, Grebogi C, Hunt BR, Yorke JA. Map with more than 100 coexisting low-period periodic attractors. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1996;54(1):71–81. DOI: 10.1103/physreve.54.71.
  2. Ikeda K, Daido H, Akimoto O. Optical turbulence: Chaotic behavior of transmitted light from a ring cavity. Phys. Rev. Lett. 1980;45(9):709–712. DOI: 10.1103/PhysRevLett.45.709.
  3. Kuznetsov AP, Turukina LV. Dynamical Systems Of Different Classes As Models Of The Kicked Non-Linear Oscillator. Izvestiya VUZ. Applied Nonlinear Dynamics. 2000;8(2):31–42.
  4. Kuznetsov AP, Kuznetsov SP, Ryskin NM. Nonlinear oscillations. Moscow: Fizmatlit; 2002. 292 p. (In Russian).
  5. Kuznetsov SP. Dynamic chaos. Moscow: Fizmatlit; 2001. 296 p. (In Russian).
  6. Carcasses J, Mira C, Bosch M, Simo C, Tatjer JC. Crossroad area – spring area transition (1) Parameter plane representation. Int. J. Bifurc. & Chaos. 1991;1:183–196.
  7. Mira C, Carcasses J. On the crossroad area – saddle area and spring area transition. Int. J. of Bif. and Chaos. 1991;1(3):641–656. DOI: 10.1142/S0218127491000464.
  8. Kuznetsov YuA, Meijer HGE, van Veen L. The fold-ip bifurcation. Int. J. of Bif. And Chaos. 2004;14(7):2253–2282.
  9. Zaslavsky GM. Stochasticity of Dynamic Systems. Moscow: Nauka; 1984. 272 p. (In Russian).
Short text (in English):
(downloads: 92)