Abstract
The interrelation between autonomous oscillations in local systems and stable dissipative structures in spatially distributed systems is analyzed. Darwinian evolution in populations comprising the ecosystem is shown to be able to cause the qualitative rearrangements of dynamic modes and smooth appearance of oscillations in local systems. The same evolutionary mechanisms analyzed within bilocal systems, may lead to appearance of dissipative structures (both smooth and sharp).
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Bazykin, A. D.: The model of population density dynamics and the problem of coexistence of closed species. Zhurnal Obshei Biologii 30, 259–264 (1969)
Keener, J. P.: Secondary bifurcation in nonlinear diffusion reaction equations. Studies in Appl. Math. 55, 187–211 (1976)
Khibnik, A. I.: Periodical solutions for the system of n differential equations. Algorithms and programmes on FORTRAN, No. 5, Pushchino 1979
Langford, W. F., Iooss, G.: Interactions of Hopf and pichfork bifurcations. In: Bifurcation problems and their numerical solution. Int. Ser. Numer. Math. 54, 103–134 (1980)
Nicolis, G., Prigogine, I.: Self-organization in non-equilibrium systems. New York: Wiley 1977
Segel, L. A., Jackson, J. L.: Dissipative structure: An explanation and an ecological example. J. Theoret. Biology 37, 545–559 (1972)
Segel, L. A., Levin, S. A.: Application of nonlinear stability theory to the study of the effects of diffusion on predator-prey interactions. Topics in statistical mechanics and biophysics: A memorial to Julius L. Jackson. Proc. AIP Conf. 27, 123–152 (1976)
Tikhonov, A. N.: Singularly perturbed systems differential equations. Matematicheskii sbornik 31 (73), 575–586 (1952)
Turing, A. M.: The chemical basis of morphogenesis. Phil. Trans. of the Royal Society of London B237, 37–72 (1952)
Vasiliev, V. A., Romanovskii, Yu. M., Yahno, V. G.: Selfwave processes in distributed kinetic systems. Uspekhi Phys. Nauk 128, 625–666 (1979)
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Bazykin, A.D., Khibnik, A.I. & Aponina, E.A. A model of evolutionary appearance of dissipative structure in ecosystems. J. Math. Biology 18, 13–23 (1983). https://doi.org/10.1007/BF00275907
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DOI: https://doi.org/10.1007/BF00275907