Geodesic
Global chaotization effect in particles chain
Russian journal of nonlinear dynamics, Tome 6 (2010) no. 2, pp. 291-305.

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The appearance of chaotic regimes near elliptic point in a cell of particles' chain interacting by means of Lennard-Jones potential is studied. The threshold nature of chaotization advent in the case of single-frequency cell excitation is demonstrated. A method of global chaotization based on multifrequency external excitation is proposed. The results of numerical experiments show that in this case the formation of global chaos is achieved at essentially lower values of external excitation amplitude and frequency, than in the case of single frequency excitation.
Keywords: nonlinear dynamics, molecular dynamics, Lennard-Jones potential, chaotic dynamics, Chirikov's criterion. 
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M. A. Guzev; Yu. G. Izrailsky; K. V. Koshel. Global chaotization effect in particles chain. Russian journal of nonlinear dynamics, Tome 6 (2010) no. 2, pp. 291-305. http://geodesic.mathdoc.fr/item/ND_2010_6_2_a4/

[1] Zaslavskii G. M., Sagdeev R. Z., Vvedenie v nelineinuyu fiziku: Ot mayatnika do turbulentnosti i khaosa, Nauka, M., 1988, 368 pp.

[2] Rom-Kedar V., Leonard A., Wiggins S., “An analytical study of transport, mixing and chaos in an unsteady vortical flow”, J. Fluid Mech., 214 (1990), 347–394 | DOI | MR | Zbl

[3] Treschev D., “Width of stochastic layers in near-integrable two-dimensional symplectic maps”, Phys. D, 116:1-2 (1998), 21–43 | DOI | MR | Zbl

[4] Zaslavskii G. M., Fizika khaosa v gamiltonovykh sistemakh, Inst. kompyutern. issled., M.–Izhevsk, 2004, 288 pp.

[5] Pikovskii A. S., “Generatsiya khaoticheskikh voln v nelineinoi tsepochke”, Pisma v ZhETF, 40:6 (1984), 217–219

[6] Makarov D. V., Uleiskii M. Yu., “Generatsiya ballisticheskogo transporta chastits pri vozdeistvii slabogo peremennogo vozmuscheniya na periodicheskuyu gamiltonovu sistemu”, Pisma v ZhETF, 83:11 (2006), 614–617

[7] Guzev M. A., Izrailskii Yu. G., Shepelov M. A., Permyakov N. A., “Struktura i khaos odnomernoi molekulyarnoi sistemy”, Fizika i khimiya stekla, 34:4 (2008), 518–528

[8] Chirikov B. V., “A universal instability of many-dimensional oscillator systems”, Phys. Rep., 52:5 (1979), 264–379 | DOI | MR

[9] Izrailsky Yu. G., Koshel K. V., and Stepanov D. V., “Determination of the optimal excitation frequency range in background flows”, Chaos, 18:1 (2008), 013107, 9 pp. | DOI | MR

[10] Koshel K. V. and Prants S. V., “Chaotic advection in the ocean”, Physics-Uspekhi, 49:11 (2006), 1151–1178 | DOI

[11] Gudimenko A. I., “Dinamika trekh vikhrei v vozmuschennykh ustoichivykh ravnostoronnei i kollinearnoi konfiguratsiyakh”, Nelineinaya dinamika, 3:4 (2007), 379–391 | Zbl

[12] Shinbrot T., Grebogi C., Yorke J. A., and Ott E., “Using small perturbations to control chaos”, Nature, 363 (1993), 411–417 | DOI

[13] Tang X. Z., Boozer A. H., “Design criteria of a chemical reactor based on a chaotic flow”, Chaos, 9:1 (1999), 183–194 | DOI

[14] Koshel K. V., Sokolovskiy M. A., and Davies P. A., “Chaotic advection and nonlinear resonances in an oceanic flow above submerged obstacle”, Fluid Dynam. Res., 40 (2008), 695–736 | DOI | MR | Zbl