Investigation of Turing structures formation under the influence of wave instability

 pdf (14888K)  / Annotation

List of references:

  1. Б. П. Белоусов. Периодически действующая реакция и ее механизм / Сборник рефератов по радиационной медицине за 1958 год. — М: Медгиз, 1959. — С. 145–147.
    • B. P. Belousov. Periodically operating reaction and its mechanism / Collection of essays on radiation medicine for 1958. — Moscow: Medgiz, 1959. — P. 145–147. — in Russian.
  2. М. Ю. Борина, А. А. Полежаев. Диффузионная неустойчивостьв трехкомпонентной модели типа «реакция – диффузия» // Компьютерные исследования и моделирование. — 2011. — Т. 3, № 2. — С. 135–146. — DOI: 10.20537/2076-7633-2011-3-2-135-146
    • M. Yu. Borina, A.A. Polezhaev. Diffusion instability in a three-component model of the reaction-diffusion type // Computer research and modeling. — 2011. — V. 3, no. 2. — P. 135–146. — in Russian. — DOI: 10.20537/2076-7633-2011-3-2-135-146
  3. М. Ю. Борина, А. А. Полежаев. Исследование механизмов формирования сегментированных волн в активных средах // Компьютерные исследования и моделирование. — 2013. — Т. 5, № 4. — С. 533–542. — DOI: 10.20537/2076-7633-2013-5-4-533-542
    • M. Yu. Borina, A. A. Polezhaev. Study of the formation mechanisms of segmented waves in active media // Computer research and modeling. — 2013. — V. 5, no. 4. — P. 533–542. — in Russian. — DOI: 10.20537/2076-7633-2013-5-4-533-542
  4. Е. Е. Гиричева. Моделирование состояния планктонного сообщества с учетом плотностнозависимой смертности и пространственной активности зоопланктона // Компьютерные исследования и моделирование. — 2016. — Т. 8, № 3. — С. 549–560. — DOI: 10.20537/2076-7633-2016-8-3-549-560
    • E. E. Giricheva. Modeling the state of plankton community with account of densitydependent mortality and spatial activity of zooplankton // Computer research and modeling. — 2016. — V. 8, no. 3. — P. 549–560. — in Russian. — DOI: 10.20537/2076-7633-2016-8-3-549-560
  5. М. Б. Кузнецов, А. А. Полежаев. Механизм образования осциллонов — уединенных колебательных структур // Компьютерные исследования и моделирование. — 2015. — Т. 7, № 6. — С. 1177–1184. — DOI: 10.20537/2076-7633-2015-7-6-1177-1184
    • M. B. Kuznetsov, A. A. Polezhaev. The mechanism of formation of oscillons — localized oscillatory structures // Computer research and modeling. — 2015. — V. 7, no. 6. — P. 1177–1184. — in Russian. — DOI: 10.20537/2076-7633-2015-7-6-1177-1184
  6. A. Nakamasu, G. Takahashi, S. Teperick, S. Kondo. Hexagon and stripe Turing structures in a gas discharge system // Physics Letters A. — 1996. — V. 211, no. 3. — P. 184–190. — DOI: 10.1016/0375-9601(95)00926-4.
  7. I. A. Berenstein. Superlattice Turing structures in a photosensitive reaction-diffusion system // Physical review letters. — 2003. — V. 91, no. 5. — 058302. — DOI: 10.1103/PhysRevLett.91.058302. — ads: 2003PhRvL..91e8302B.
  8. W. Mazin, K. Rasmussen, E. Mosekilde, P. Borckmans. Experimental evidence of a sustained standing Turing-type nonequilibrium chemical pattern // Physical Review Letters. — 1990. — V. 64, no. 24. — P. 2953–2956. — DOI: 10.1103/PhysRevLett.64.2953.
  9. M. A. Dolnik. Standing Waves in a Two-Dimensional Reaction- Diffusion Model with the Short-Wave Instability // The Journal of Physical Chemistry A. — 1999. — V. 103, no. 1. — P. 38–45. — DOI: 10.1021/jp982771j. — ads: 1999JPCA..103...38D.
  10. A. Koch, H. Meinhardt. Biological pattern formation: from basic mechanisms to complex structures // Reviews of modern physics. — 1994. — V. 66, no. 4. — P. 1481. — DOI: 10.1103/RevModPhys.66.1481. — MathSciNet: MR2691472. — ads: 1994RvMP...66.1481K.
  11. M. A. Kuznetsov. Pattern formation in a reaction-diffusion system of Fitzhugh-Nagumo type before the onset of subcritical Turing bifurcation // Physical Review E. — 2017. — V. 95, no. 5. — 052208. — DOI: 10.1103/PhysRevE.95.052208. — MathSciNet: MR3797860. — ads: 2017PhRvE..95e2208K.
  12. A. Mamaev, M. Saffman. Pattern formation in a linear photorefractive oscillator // Optics communications. — 1996. — V. 128, no. 4-6. — P. 281–286. — DOI: 10.1016/0030-4018(96)00158-7. — ads: 1996OptCo.128..281M.
  13. W. A. Mazin. Pattern formation in the bistable Gray – Scott model // Mathematics and Computers in Simulation. — 1996. — V. 40, no. 3-4. — P. 371–396. — DOI: 10.1016/0378-4754(95)00044-5.
  14. M. A. Meixner. Generic spatiotemporal dynamics near codimension-two Turing-Hopf bifurcations // Physical Review E. — 1997. — V. 55, no. 6. — P. 6690. — DOI: 10.1103/PhysRevE.55.6690. — MathSciNet: MR1453807. — ads: 1997PhRvE..55.6690M.
  15. Q. Ouyang, H. L. Swinney. Interactions between zebrafish pigment cells responsible for the generation of Turing patterns // Proceedings of the National Academy of Sciences. — 2009. — V. 106, no. 21. — P. 8429–8434. — DOI: 10.1073/pnas.0808622106.
  16. A. M. Nesterenko. Morphogene adsorption as a Turing instability regulator: Theoretical analysis and possible applications in multicellular embryonic systems // PloS one. — 2017. — V. 12, no. 2. — e0171212. — DOI: 10.1371/journal.pone.0171212.
  17. E. M. Nicola. Drifting pattern domains in a reaction-diffusion system with nonlocal coupling // Physical Review E. — 2002. — V. 65, no. 5. — 055101. — DOI: 10.1103/PhysRevE.65.055101. — ads: 2002PhRvE..65e5101N.
  18. V. Castets, E. Dulos, J. Boissonade, P. P. De Kepper. Transition from a uniform state to hexagonal and striped Turing patterns // Nature. — 1991. — V. 352, no. 6336. — P. 610.
  19. P. F. Pelz. Similar size of slums caused by a Turing instability of migration behavior // Physical Review E. — 2019. — V. 99, no. 2. — 022302. — DOI: 10.1103/PhysRevE.99.022302. — ads: 2019PhRvE..99b2302P.
  20. I. A. Prigogine. Symmetry breaking instabilities in dissipative systems. II // The Journal of Chemical Physics. — 1968. — V. 48, no. 4. — P. 1695–1700. — DOI: 10.1063/1.1668896. — ads: 1968JChPh..48.1695P.
  21. H. A. Shoji. Stripe // Journal of theoretical biology. — 2003. — V. 224, no. 3. — P. 339–350. — DOI: 10.1016/S0022-5193(03)00170-X. — MathSciNet: MR2067242.
  22. A. Mamaev, M. Saffman. Dissipation and displacement of hotspots in reaction-diffusion models of crime // Proceedings of the National Academy of Sciences. — 2010. — V. 107, no. 9. — P. 3961–3965. — DOI: 10.1073/pnas.0910921107.
  23. A. M. Turing. The chemical basis of morphogenesis // Bulletin of mathematical biology. — 1990. — V. 52, no. 1-2. — P. 153–197. — DOI: 10.1007/BF02459572.
  24. V. K. Vanag. Comparative analysis of packet and trigger waves originating from a finite wavelength instability // The Journal of Physical Chemistry A. — 2002. — V. 106, no. 46. — P. 11394–11399. — DOI: 10.1021/jp026081y. — ads: 2002JPCA..10611394V.
  25. V. K. Vanag. Diffusive instabilities in heterogeneous systems // The Journal of chemical physics. — 2003. — V. 119, no. 14. — P. 7297–7307. — DOI: 10.1063/1.1606677. — ads: 2003JChPh.119.7297V.
  26. V. K. Vanag. Subcritical wave instability in reaction-diffusion systems // The Journal of chemical physics. — 2004. — V. 121, no. 2. — P. 890–894. — DOI: 10.1063/1.1760742. — ads: 2004JChPh.121..890V.
  27. V. K. Vanag. Resonance-induced oscillons in a reaction-diffusion system // Physical Review E. — 2006. — V. 73, no. 1. — 016201. — DOI: 10.1103/PhysRevE.73.016201. — ads: 2006PhRvE..73a6201V.
  28. H. A. Willebrand. Experimental Observation of Simultaneously Existing Moving and Standing Patterns in a Gas-Discharge System // Contributions to Plasma Physics. — 1992. — V. 32, no. 2. — P. 57–68. — DOI: 10.1002/ctpp.2150320202. — ads: 1992CoPP...32...57W.
  29. L. A. Yang. Pattern formation arising from interactions between Turing and wave instabilities // The Journal of chemical physics. — 2002. — V. 117, no. 15. — P. 7259–7265. — DOI: 10.1063/1.1507110. — ads: 2002JChPh.117.7259Y.
  30. L. A. Yang. Oscillatory Turing patterns in reaction-diffusion systems with two coupled layers // Physical review letters. — 2003. — V. 90, no. 17. — 178303. — DOI: 10.1103/PhysRevLett.90.178303. — ads: 2003PhRvL..90q8303Y.
  31. L. A. Yang. Jumping solitary waves in an autonomous reaction-diffusion system with subcritical wave instability // Physical Chemistry Chemical Physics. — 2006. — V. 8, no. 40. — P. 4647–4651. — DOI: 10.1039/B609214D.
  32. A. M. Zhabotinsky. Pattern formation arising from wave instability in a simple reaction-diffusion system // The Journal of chemical physics. — 1995. — V. 103, no. 23. — P. 10306–10314.

Indexed in Scopus

Full-text version of the journal is also available on the web site of the scientific electronic library eLIBRARY.RU

The journal is included in the Russian Science Citation Index

The journal is included in the RSCI

International Interdisciplinary Conference "Mathematics. Computing. Education"