Complex behavior of a trajectory in single- and double-frequency systems

International Applied Mechanics

Volumn 41, Issue 3, 2005, Pages 315-323

  Martynyuk, A A ^a   Nikitina, N V ^a  

^a S P TIMOSHENKO INSTITUTE OF MECHANICS   (Ukraine)

Author keywords

Closed curves; Complex behavior of trajectory; Symmetry

Indexed keywords

CLOSED CURVES; COMPLEX BEHAVIOR OF TRAJECTORIES; NOVELTY; SYMMETRY;

ENERGY DISSIPATION; FOURIER TRANSFORMS; HARMONIC ANALYSIS; HEAT EXCHANGERS; MAGNETIC FIELDS; MATHEMATICAL MODELS; OPTIMIZATION; SPECTRUM ANALYSIS; VECTORS;

OSCILLATIONS;

EID: 23744446589     PISSN: 10637095     EISSN: 15738582     Source Type: Journal    
DOI: 10.1007/s10778-005-0090-8     Document Type: Article

References (18)

1. V. S. Anishchenko, Complex Oscillations in Simple Systems: Mechanisms, Structure, and Properties of Chaos in Radiophysical Systems [in Russian], Nauka, Moscow (1990).
2. V. I. Arnol'd, Ordinary Differential Equations [in Russian], Glavn. Red. Fiz.-Mat. Lit., Moscow (1984).
3. N. N. Bogolyubov and Yu. A. Mitropol'skii, Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1974).
4. V. I. Zubov, Oscillations and Waves [in Russian], Izd. Leningr. Univ., Leningrad (1989).
5. A. A. Martynyuk and N. V. Nikitina, "Complex oscillations revisited," Int. Appl. Mech., 41, No. 2, 179-186 (2005).
6. Yu. A. Mitropol'skii, Nonlinear Mechanics: Single-Frequency Oscillations [in Russian], Inst. Mat. NAN Ukrainy, Kiev (1997).
7. V. V. Nemytskii and V. V. Stepanov, Qualitative Theory of Differential Equations [in Russian], GITTL, Moscow (1949).
8. M. I. Rabinovich and D. I. Trubetskov, An Introduction to the Theory of Oscillations and Waves [in Russian], NITs Regul. Khaotich. Dinam., Moscow (2000).
9. L. P. Shil'nikov, A. L. Shil'nikov, D. V. Turaev, and L. Chua, Qualitative Methods in Nonlinear Dynamics [in Russian], Pt. 1, Inst. Komp. Issled., Moscow (2004).
10. B. Aulbach and B. M. Kieninger, "On three definitions of chaos," Nonlin. Dynam. Syst. Theor., 1, No. 1, 23-38 (2001).
11. M-P. Boer, B. W. Kooi, and S. A. L. M. Kooijman, "Homoclinic and heteroclinic orbits to a cycle in a tri-trophic food chain," J. Vath. Biol., 39, No. 1, 19-38 (1999).
12. A. A. Martynyuk and N. V. Nikitina, "Bistable oscillator theory revisited," Int. Appl. Mech., 38, No. 4, 489-497 (2002).
13. A. A. Martynyuk and N. V. Nikitina, "On an approximate solution of the Van der Pol equations with a large parameter," Int. Appl. Mech., 38, No. 8, 1017-1023 (2002).
14. A. A. Martynyuk and N. V. Nikitina, "A note on bifurcations of motions in the Lorenz system," Int. Appl. Mech., 39, No. 2, 224-231 (2003).
15. A. A. Martynyuk and N. V. Nikitina, "Saddle limit cycles in the Lorenz system," Int. Appl. Mech., 39, No. 5, 613-620 (2003).
16. A. A. Martynyuk and N. V. Nikitina, "Studying the complex oscillations of a star in the field of a galaxy," Int. Appl. Mech., 40, No. 4, 453-461 (2004).
17. V. Reitman, Reguläre und chaotische Dynamik, Teubner, Leipzig (1996).
18. Y. Shinohara, "A geometric method for the numerical solution of non-linear equations and its application to non-linear oscillations," Publ. Res. Inst. Math. Sci.,Kyoto Univ., 8, No. 1, 13-42 (1972).