The simplest model of targeted migration
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 1, pp. 3-17.

Voir la notice de l'article provenant de la source Math-Net.Ru

A simple model of targeted migration is studied. The model implies the global information access of the beings migrating from station to station. This approximation yields a special class of models which generater a semi-group. Various dynamic regimes, as well as the stability conditions are studied. Some further expansions of the modelling based on evolution optimality principle are considered.
Keywords: optimality, selection, projection, maximization, stability
Mots-clés : information.
@article{JSFU_2012_5_1_a0,
     author = {Michael G. Sadovsky},
     title = {The simplest model of targeted migration},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {3--17},
     publisher = {mathdoc},
     volume = {5},
     number = {1},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2012_5_1_a0/}
}
TY  - JOUR
AU  - Michael G. Sadovsky
TI  - The simplest model of targeted migration
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2012
SP  - 3
EP  - 17
VL  - 5
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2012_5_1_a0/
LA  - en
ID  - JSFU_2012_5_1_a0
ER  - 
%0 Journal Article
%A Michael G. Sadovsky
%T The simplest model of targeted migration
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2012
%P 3-17
%V 5
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2012_5_1_a0/
%G en
%F JSFU_2012_5_1_a0
Michael G. Sadovsky. The simplest model of targeted migration. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 1, pp. 3-17. http://geodesic.mathdoc.fr/item/JSFU_2012_5_1_a0/

[1] V. Volterra, “Variazioni e fluttuazioni del numero d'individui in specie animali conviventi”, Mem. R. Accad. Naz. dei Lincei Ser. VI, 2 (1926), 31–113

[2] V. Volterra, Leçons sur la théorie mathèmatique de la lutte pour la vie, Gauthier-Villars, Paris, 1931 | Zbl

[3] A. J. Lotka, Elements of Physical Biology, Williams Wilkens, Baltimore, 1925 | Zbl

[4] P. Turchin, Complex Population Dynamics: A Theoretical/Empirical Synthesis, Princeton University Press, 2003 | MR | Zbl

[5] Dieckmann U., Law R., Metz J. A. J. (eds.), The geometry of ecological interactions: simplifying spatial complexity, Cambridge University Press, Cambridge, UK

[6] A. A. Berryman, Population cycles: the case for trophic interactions, Oxford University Press, New York, 2002

[7] A. A. Berryman, “On principles, laws and theory in population ecology”, Oikos, 103 (2003), 695–701 | DOI

[8] D. Alstad, Basic Populus Models of Ecolog, Prentice Hall, 2001

[9] J. D. Murray, Mathematical Biology, v. I–II, Third edition, Springer-Verlag, Berlin, 2002 | MR

[10] H. R. Thieme, Mathematics in Population Biology, Princeton Series in Theoretical and Computational Biology, Princeton Univ. Press, 2003 | MR | Zbl

[11] L. Edelstein, K. Edelstein, Mathematical Models in Biology, Birkheauser Mathematics Series, 1988 | MR

[12] R. Bernstein, Population Ecology: An Introduction to Computer Simulations, Wiley Sons, 2003

[13] L. R. Ginzburg, M. Colyvan, Ecological Orbits: how planets move and populations grow, Oxford University Press, New York, 2004

[14] H. Pastijn, “Chaotic Growth with the Logistic Model of P.-F. Verhulst”, The Logistic Map and the Route to Chaos, Book Series: Understanding Complex Systems, Springer, Berlin–Heidelberg, 2006, 3–11 | MR | Zbl

[15] Xinfu Chen, R.Hambrock, Yuan Lou, “Evolution of conditional dispersal: a reaction-diffusion-advection model”, Journal of Mathematical Biology, 57 (2008), 361–386 | DOI | MR | Zbl

[16] K. Smitalova, S. Sujan, A mathematical treatment of dynamical models in biological science, Ellis Horwood, 1991 | MR | Zbl

[17] A. N. Kolmogorov, I. G. Petrowsky, N. A. Piscounov, “Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique”, Mosc. Univ. Bull. Math. (1), 1937, no. 6, 1–25 | Zbl

[18] R. Law, D. J. Murrell, U. Dieckmann, “Population growth in space and time: spatial logistic equations”, Ecology, 84:1 (2003), 252–262 | DOI | MR

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

[20] 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

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

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

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

[24] 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

[25] 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

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

[27] J. B. S. Haldane, The Causes of Evolution, Princeton Science Library, Princeton University Press, 1990

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

[29] A. N. Gorban, Equilibrium encircling. Equations of chemical kinetics and their thermodynamic analysis, Nauka, Novosibirsk, 1984 | MR

[30] A. N. Gorban, Selection theorem for systems with inheritance, 2005, arXiv: cond-mat/0405451 | MR

[31] F. N. Semevsky, S. M. Semenov, Mathematical modelling of ecological processes, Gidrometeoizdat, Leningrad, 1984

[32] 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

[33] L. I. Rozonoer, E. I. Sedyh, “On the mechanisms of evolution of self-reproduction systems, 1”, Automation and Remote Control, 40:2 (1979), 243–251

[34] Sov. Phys.-Usp., 17:6 (1975), 896–919 | DOI | DOI

[35] V. E. Zakharov, V. S. L'vov, G. E. Falkovich, Kolmogorov spectra of turbulence, v. 1, Wave Turbulence, Springer, Berlin, 1992

[36] V. S. L'vov, Wave turbulence under parametric excitation applications to magnets, Springer, Berlin–Heidelberg, 1994 | MR

[37] A. B. Ezersky, M. I. Rabinovich, “Nonlinear-wave competition and anisotropic spectra of spatiotemporal chaos of Faraday ripples”, Europhysics Letters, 13:3 (1990), 243–249 | DOI

[38] A. N. Gorban, I. V. Karlin, “Family of additive entropy functions out of thermodynamic limit”, Physical Review E, 67 (2003), 016104 | DOI | MR

[39] M. E. Gilpin, F. J. Ayala, “Global models of growth and competition”, Proc. Natl. Acad. Sci., 70 (1973), 3590–3593 | DOI | Zbl

[40] A. N. Gorban, R. G. Khlebopros, Demon of Darwin: Idea of optimality and natural selection, Nauka (FizMatGiz), Moscow, 1988

[41] 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

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

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

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

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

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

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

[48] 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

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

[50] S. A. Levin, B. Grenfell, A. Hastings, A. S. Perelson, “Mathematical and Computational Challenges in Population Biology and Ecosystems Science”, Science, 275 (1997), 334–343 | DOI | Zbl

[51] S. K. Heinz, E. Strand, “Adaptive Patch Searching Strategies in Fragmented Landscapes”, Evolutionary Ecology, 20 (2006), 113–130 | DOI

[52] R. Lande, S. Engen, B.-E. Sæther, Stochastic Population Dynamics in Ecology and Conservation, Oxford Series in Ecology and Evolution, Oxford Univ. Press, 2003

[53] P. A. Brychev, M. G. Sadovsky, M. Yu. Senashova, “Local information accessibility in modelling of optimal migration”, Doklady Mathematics, 80:1 (2009), 627–629 | MR | Zbl

[54] L. Jaulin, M. Kieffer, O. Didrit, E. Walter, Applied Interval Analysis, with Examples in Parameter and State Estimation, Robust Control and Robotics, Springer-Verlag, Heidelberg–Hamburg, 2001 | MR

[55] M. S. Petkovic, L. D. Petkovic, Complex Interval Arithmetic and Its Applications, John Wiley, 1998

[56] W. Krämer, J. W. von Gudenberg, Scientific Computing, Validated Numerics, Interval Methods, Kluwer, 2001

[57] U. W. Kulisch, Advanced Arithmetic for the Digital Computer, Springer-Verlag, Wien, 2002 | MR | Zbl

[58] A. Neumaier, Introduction to Numerical Analysis, Cambridge Univ. Press, Cambridge, 2001 | MR | Zbl