Waves in systems with cross-diffusion as a new class of nonlinear waves

M.A. Tsyganov^a, V.N. Biktashev^b, J. Brindli^c, A.V. Holden^d, G.R. Ivanitskii^a
^aInstitute for Theoretical and Experimental Biophysics, Russian Academy of Sciences, Institutskaya str. 3, Pushchino, Moscow Region, 142290, Russian Federation
^bDepartment of Mathematical Sciences, University of Liverpool, Liverpool, UK
^cDepartment of Applied Mathematics, University of Leeds, Leeds, UK
^dFaculty of Biological Sciences, University of Leeds, Leeds, UK

Research on spatially extended excitable systems with cross-diffusion components is reviewed. Particular attention is given to the new phenomena of the quasi-soliton and half-soliton interaction of excitation waves, which are specific to such systems and occur along with the standard nonsoliton wave interaction that causes the waves to mutually annihilate. A correlation is shown to exist between interaction regimes and wave profile shapes. One example of a cross-diffusion system is population systems with taxes. Based on the mathematical models of and experimental work with bacterial populations, waves in excitable cross-diffusion systems can be identified as a new class of nonlinear waves.

PACS: 05.45.−a, 87.18.Hf, 87.23.Cc (all)
DOI: 10.1070/PU2007v050n03ABEH006114
URL: https://ufn.ru/en/articles/2007/3/b/
Web of Science

000248004300002
Scopus

2-s2.0-34547251534
ADS NASA

2007PhyU...50..263T
Citation: Tsyganov M A, Biktashev V N, Brindli J, Holden A V, Ivanitskii G R "Waves in systems with cross-diffusion as a new class of nonlinear waves" Phys. Usp. 50 263–286 (2007)

BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Цыганов М А, Бикташев В Н, Бриндли Дж, Холден А В, Иваницкий Г Р «Волны в кросс-диффузионных системах — особый класс нелинейных волн» УФН 177 275–300 (2007); DOI: 10.3367/UFNr.0177.200703b.0275

References (169) Cited by (52) Similar articles (20) ↓

G.R. Ivanitskii, A.B. Medvinskii, M.A. Tsyganov “From the dynamics of population autowaves generated by living cells to neuroinformatics” Phys. Usp. 37 961–989 (1994)
G.R. Ivanitskii, A.B. Medvinskii, M.A. Tsyganov “From disorder to order as applied to the movement of micro-organisms” Sov. Phys. Usp. 34 (4) 289–316 (1991)
G.R. Ivanitskii “The self-organizing dynamic stability of far-from-equilibrium biological systems” Phys. Usp. 60 705–730 (2017)
V.V. Klinshov, V.I. Nekorkin “Synchronization of delay-coupled oscillator networks” Phys. Usp. 56 1217–1229 (2013)
V.K. Vanag “Waves and patterns in reaction-diffusion systems. Belousov-Zhabotinsky reaction in water-in-oil microemulsions” Phys. Usp. 47 923–941 (2004)
G.R. Ivanitskii, A.B. Medvinskii et al “From Maxwell’s demon to the self-organization of mass transfer processes in living systems” Phys. Usp. 41 1115–1126 (1998)
G.N. Borisyuk, R.M. Borisyuk et al “Models of neural dynamics in brain information processing — the developments of ’the decade’” Phys. Usp. 45 1073–1095 (2002)
G.R. Ivanitskii “21st century: what is life from the perspective of physics?” Phys. Usp. 53 327–356 (2010)
F.I. Ataullakhanov, V.I. Zarnitsyna et al “A new class of stopping self-sustained waves: a factor determining the spatial dynamics of blood coagulation” Phys. Usp. 45 619–636 (2002)
A.B. Medvinskii, S.V. Petrovskii et al “Spatio-temporal pattern formation, fractals, and chaos in conceptual ecological models as applied to coupled plankton-fish dynamics” Phys. Usp. 45 27–57 (2002)
D.S. Chernavskii “The origin of life and thinking from the viewpoint of modern physics” Phys. Usp. 43 151–176 (2000)
M.I. Rabinovich, M.K. Muezzinoglu “Nonlinear dynamics of the brain: emotion and cognition” Phys. Usp. 53 357–372 (2010)
Yu.M. Romanovskii, V.A. Teplov “The physical bases of cell movement. The mechanisms of self-organisation of amoeboid motility” Phys. Usp. 38 521–542 (1995)
M.B. Menskii “Concept of consciousness in the context of quantum mechanics” Phys. Usp. 48 389–409 (2005)
L.V. Doronina-Amitonova, I.V. Fedotov et al “Neurophotonics: optical methods to study and control the brain” Phys. Usp. 58 345–364 (2015)
A. Loskutov “Fascination of chaos” Phys. Usp. 53 1257–1280 (2010)
A.Yu. Morozov “Integrability and matrix models” Phys. Usp. 37 1–55 (1994)
V.S. Anishchenko, S.V. Astakhov “Poincaré recurrence theory and its applications to nonlinear physics” Phys. Usp. 56 955–972 (2013)
O.V. Maslennikov, V.I. Nekorkin “Adaptive dynamical networks” Phys. Usp. 60 694–704 (2017)
H.D. Abarbanel, M.I. Rabinovich et al “Synchronisation in neural networks” Phys. Usp. 39 337–362 (1996)

The list is formed automatically.