Spatially inhomogeneous periodic solutions in distributed Hutchinson equation
Modelirovanie i analiz informacionnyh sistem, Tome 16 (2009) no. 4, pp. 77-85.

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The asymptotics of spatially inhomogeneous periodic solutions of the complex spatially distributed Hutchinson equation with periodic boundary conditions are presented. It is shown that such solutions are observable in a numerical experiment.
Keywords: asymptotic methods, distributed Hutchinson equation, method of steps.
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S. D. Glyzin; S. A. Kashchenko; A. S. Polstyanov. Spatially inhomogeneous periodic solutions in distributed Hutchinson equation. Modelirovanie i analiz informacionnyh sistem, Tome 16 (2009) no. 4, pp. 77-85. http://geodesic.mathdoc.fr/item/MAIS_2009_16_4_a6/

[1] E. M. Wright, “A non-linear difference- differential equation”, J. Reine Angew. Math., 194 (1955) | MR | Zbl

[2] S. Kakutani, L. Markus, “On the non-linear difference-differential equation $y'(t)=\{A-By(t-\tau)\}y(t)$”, Contributions to the Theory of Non-linear Oscillations IV, Annals of Math. Studies, 41, Prinston University Press, Prinston, 1958 | MR

[3] Robert M. May, Stability and complexity in Model ecosystems, Prinston, New-Jersey, 1973

[4] R. E. Bellman, A survey of the mathematical theory of time-lag, retarded control, and hereditary processes, the Rand Corporation, Santa Monica, California, 1954 | MR

[5] S. A. Kaschenko, “Asimptotika periodicheskogo resheniya obobschennogo uravneniya Khatchinsona”, Issledovaniya po ustoichivosti i teorii kolebanii, Yaroslavl, 1981

[6] S. A. Kaschenko, “Prostranstvenno-neodnorodnye struktury v prosteishikh modelyakh s zapazdyvaniem i diffuziei”, Matematicheskoe modelirovanie, 2:9 (1990), 49–69 | MR | Zbl

[7] A. Yu. Kolesov, N 1, IMK, Vilnyus, 1985

[8] M. Bestehorn, E. V. Grigorieva, S. A. Kaschenko, “Spatio-temporal structures in a biological model with delay and diffusion”, The Third International Conference “Tools for mathematical modelling” (18–23 June 2001, Saint Petersburg)

[9] S. A. Kaschenko, Issledovanie asimptotiki periodicheskikh reshenii avtonomnykh parabolicheskikh uravnenii s maloi diffuziei, Dep. VINITI 15.01.85 No 388-85, 26 pp.

[10] Dzh. Kheil, Teoriya funktsionalno-differentsialnykh uravnenii, Mir, M., 1984 | MR