Abstract
We consider that a population of individuals governed by the Nagumo model is characterized by predisposition towards aggregation. “Dissipative solitons” interacting are solutions for such system. We changed the possibility of extinction, predicted by Nagumo model, by a uniform background of low population’s density and then we observed relevant effect on interaction between “solitons”.
Similar content being viewed by others
References
A.M. Moya, in La génesis de la complejidad biológica, edited by E. Molina (Universidad de Zaragosa, Spain, 1996), pp. 111–122
M.E. Boraas, D.B. Seale, J.E. Boxhorn, Evolutionary Ecology 12, 153 (1998)
J.H. Koschwanez, K.R. Foster, A.W. Murray, PLoS Biol. 9, e1001122 (2011)
T. Pitcher, A. Magurran, I. Winfield, Behav. Ecol. Sociobiol. 10, 149 (1982)
B. Partridge, J. Johansson, J. Kalish, Environ. Biol. Fishes 9, 253 (1983)
F. Fish, J. Exp. Zoology 273, 1 (1995)
H. Milinski, R. Heller, Nature 275, 642 (1978)
G. Roberts, Animal Behav. 51, 1077 (1996)
S. Lima, Animal Behav. 49, 11 (1995)
W.D. Hamilton, J. Theor. Biol. 31, 295 (1971)
G. Turner, T. Pitcher, Am. Naturalist 128, 228 (1986)
R.G. Krause, J.D. Rubenstein, J. Fish Biol. 52, 494 (1998)
R.D. Alexander, Ann. Rev. Ecol. Syst. 5, 325 (1974)
B.C.R. Bertram, in Living in groups: predators and prey, Behavioral Ecology, 1st edn., edited by R. Krebs, N.B. Davies (Blackwell Scientific, Oxford, 1978), pp. 64–96
D.I. Rubenstein, Perpesptives Ethology 3, 205 (1978)
D.J. Hoare, I.D. Couzin, J.G.J. Godin, J. Krause, Animal Behav. 67, 155 (2004)
M. Abrahams, P. Colgan, Environ. Biol. Fishes 13, 195 (1985)
B. Partridge, T. Pitcher, M. Cullen, J. Wilson, Behav. Ecol. Sociobiol. 6, 277 (1980)
S.M. Rogers, T. Matheson, E. Despland, T. Dodgson, M. Burrows, S.J. Simpson, J. Exp. Biol. 206, 3991 (2003)
G.D. Ruxton, T.N. Sherratt, Proc. R. Soc. B 273, 2417 (2006)
S.E. Mangioni, Eur. Phys. J. B 86, 390 (2013)
J.D. Murray, Mathematical Biology, 2nd edn. (Springer, New York, 1993)
M. Cross, H. Greenside, Pattern formation and dynamics in nonequilibrium systems (Cambridge UP, Cambridge, 2009)
Localized states in physics: Solitons and patterns, edited by O. Descalzi et al. (Springer, Berlin, 2011)
A.W. Liehr, Dissipative solitons in reaction diffusion systems: Mechanisms, dynamics, interaction (Springer, Berlin, 2013)
Localized excitations in nonlinear complex systems: Current state of the art and future perspectives, edited by R. Carretero-González et al. (Springer, Berlin, 2014)
Magnetic Bubbles, edited by T.H. ODell (Wiley, New York, 1074)
M. Herschkowitz-Kaufman, G. Nicolis, J. Chem. Phys. 56, 1890 (1972)
J. Wu, R. Keolian, I. Rudnick, Phys. Rev. Lett. 52, 1421 (1984)
A. Gierer, H. Meinhardt, Kybernetik 12, 30 (1972)
A. Yochelis, A. Garfinkel, Phys. Rev. E 77, 035204 (2008)
D. Iron, M.J. Ward, Math. Comput. Simul. 55, 419 (2001)
D. Iron, M.J. Ward, J. Wei, Physica D 150, 25 (2001)
P. Coullet, C. Riera, C. Tresser, Phys. Rev. Lett. 84, 3069 (2000)
P. Coullet, Int. J. Bifurc. Chaos Appl. Sci. Eng. 12, 2445 (2002)
B. Denardo et al., Phys. Rev. Lett. 68, 1730 (1992)
W. Zhang, J. Viñals, Phys. Rev. Lett. 74, 690 (1995)
S. Longhi, Phys. Rev. E 53, 5520 (1996)
X. Wang, R. Wei, Phys. Rev. E 57, 2405 (1998)
I.V. Barashenkov, E.V. Zemlyanaya, Phys. Rev. Lett. 83, 2568 (1999)
K. Kawasaki, T. Ohta, Physica A 116, 573 (1982)
M.G. Clerc, S. Coulibaly, D. Laroze, Phys. Rev. E 77, 056209 (2008)
M.G. Clerc, S. Coulibaly, L. Gordillo, N. Mujica, R. Navarro, Phys. Rev. E 84, 036205 (2011)
M.G. Clerc, D. Escaff, V.M. Kenkre, Phys. Rev. E 72, 056217 (2005)
D. Escaff, Eur. Phys. J. D 62, 33 (2011)
W.C. Allee, Animal Aggregations: A Study in General Sociology (University Chicago Press, Chicago, 1931)
W.C. Allee, The Social Life of Animals (Beacon Press, Boston, 1938)
B. Perthame, Transport Equations in Biology, Frontiers in Mathematics (Springer-Verlag, New York, 2008)
Wei Wang, Xinlong Wang, Junyi Wang, Rongjue Wei, Phys. Lett. A 219, 74 (1996)
M.G. Clerc, S. Coulibaly, N. Mujica, R. Navarro, T. Sauma, Philos. Trans. R. Soc. A 367, 3213 (2009)
S.E. Mangioni, Physica A 391, 113 (2012)
S.E. Mangioni, H.S. Wio, Phys. Rev. E 71, 056203 (2005)
S.E. Mangioni, R.R. Deza, Phys. Rev. E 82, 042101 (2010)
S.E. Mangioni, R.R. Deza, Physica A 391, 4191 (2012)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mangioni, S. Interaction between “dissipative solitons” stabilized by aggregation in excitable kinetics. Eur. Phys. J. B 87, 248 (2014). https://doi.org/10.1140/epjb/e2014-50386-7
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2014-50386-7