Geodesic
Local information access may cause a~chaos in migration
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 1, pp. 105-113.

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A novel model of the targeted migration of a population separated into two subpopulations is proposed. The model is implemented for the local information access. Migration is not random and yields the maximization of a net reproduction, in general; specific version of this general rule is proposed. The local information access means the total lack of knowledge on the environmental conditions and transfer cost at the immigration station, for beings occupying the given station. Various regimes for the models are studied. A reciprocal chaotic-like migrations may take place, for some reasonable parameters figures.
Keywords: recurrent equation, optimality, stability, model. 
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Michael G. Sadovsky; Maria Yu. Senashova. Local information access may cause a~chaos in migration. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 1, pp. 105-113. http://geodesic.mathdoc.fr/item/JSFU_2013_6_1_a10/

[1] M. A. McPeekand, R. D. Holt, “The Evolution of Dispersal in Spatially and Temporally Varying Environments”, Am. Nat., 140 (1992), 1010 | DOI

[2] R. Condit, P. S. Ashton, P. Baker, S. Bunyavejchewin, S. Gunatilleke, N. Gunatilleke, S. P. Hubbell, R. B. Foster, A. Itoh, J. V. LaFrankie, Hua Seng Lee, E. Losos, N. Manokaran, R. Sukumar, T. Yamakura, “Spatial patterns in the distribution of tropical tree species”, Science, 288 (2000), 1414–1418 | DOI

[3] J. L. Maron, S. Harrison, “Spatial Pattern Formation in an Insect Host-Parasitoid System”, Science, 278 (1997), 1619–1621 | DOI

[4] P. Soares, M. Tomé, “Distance-dependent competition measures for eucalyptus plantations in Portugal”, Annals of Forestry Science, 56 (1999), 307–319 | DOI

[5] A. N. Gorban, M. G. Sadovsky, “Population mechanisms of cell aggregation in continuous cultivation systems”, Biotechnology and Biotechnique, 2:5 (1987), 34–36

[6] M. G. Sadovsky, Yu. L. Gurevich, N. S. Manukovsky, “Kinetics of cell aggregation in continuous cultivation”, Dynamics of chemical and biological systems, Nauka, Novosibirsk, 1989, 134–158 (in Russian)

[7] P. R. Levitt, “General kin selection models for genetic evolution of sib altruism in diploid and haplodiploid species”, Proc. Nat. Acad. Sci. USA, 72:11 (1975), 4531–4535 | DOI

[8] J. E. Straßmann, Yong Zhu, D. C. Queller, “Altruism and social cheating in the social amoeba. Dictyostelium discoideum”, Nature, 408 (2000), 965–967 | DOI

[9] A. N. Gorban, “Dynamical systems with inheritance”, Some problems of community dynamics, ed. R. G. Khlebopros, Nauka, Novosibirsk, 1992, 40–72 (in Russian) | Zbl

[10] A. N. Gorban, Equilibrium encircling. Equations of chemical kinetics and their thermodynamic analysis, Nauka, Novosibirsk, 1984 (in Russian) | MR

[11] A. N. Gorban, Systems with inheritance: dynamics of distributions with conservation of support, natural selection and finite-dimensional asymptotics, 2005, arXiv: cond-mat/0405451

[12] F. N. Semevsky, S. M. Semenov, Mathematical modelling of ecological processes, Gidrometeoizdat, Leningrad, 1984 (in Russian)

[13] M. Gromov, A dynamical model for synchronisation and for inheritance in microevolution: a survey of papers of A. Gorban, The talk given in the IHES seminar “Initiation to functional genomics: biological, mathematical and algorithmical aspects”, Institut Henri Poincaré, November 16, 2000

[14] A. N. Gorban, M. G. Sadovsky, “Optimization models of spatially distributed populations: Alle's effect”, Rus. J. General Biol., 50:1 (1989), 66–72 (in Russian)

[15] A. N. Gorban, M. G. Sadovsky, “Optimization models: the case of globally informed individuals”, Problems of environmetnal monitoring and modelling of ecosystems, 11, Gidrometeoizdat, Leningrad, 1989, 198–203 (in Russian)

[16] M. G. Sadovsky, “Optimization modelling of globally informed individuals”, Mathematical modelling in biology and chemistry. Evolution approach, Nauka, Novosibirsk, 1992, 36–67 (in Russian)

[17] M. G. Sadovsky, “The Simplest Model of Targeted Migration”, Journal SFU. Mathematics and Physics, 5:1 (2012), 3–17

[18] P. Verhulst, “Recherches mathématiques sur la loi d'accroissement de la population”, Nouv. Mém.de l'Academie Royale des Sci. et Belles-Lettres de Bruxelles, 18 (1845), 1–41

[19] A. N. Sharkovsky, “On cycles and the structure of continuous mapping”, Ukranian mathematical journal, 17:3 (1965), 104–111 (in Russian) | DOI | MR

[20] A. N. Sharkovsky, “Difference equations and population dynamics”, Mathematical methds in biology, Proc. 2nd Ukranian Conf., Naukova Dumka plc., Kiev, 1983, 143–156 (in Russian)

[21] A. Castro-e-Silva, A. T. Bernardes, “Analysis of chaotic behaviour in the population dynamics”, Physica A, 301 (2001), 63–70 | DOI | Zbl

[22] R. M. May, “Simple mathematical models with very complicated dynamics”, Nature, 261 (1976), 459–467 | DOI

[23] H. N. Matsuda, A. Ogita, A. Sasaki, K. Sato, “Statistical mechanics of population: the lattice Lotka–Volterra model”, Progress in Theoretical Physics, 88 (1992), 1035–1049 | DOI