V Belozyorov - Hierarchical heterogenity of populations modeling by the openeigen hypercycle - страница 4
0 < m < Mi,
then all populations survive and occupy only part of ecological niche; a volume of this niche is N(1 + ai + aia2 + ... + a • ... • an_ ) < So.
Mi < M < то,
then populations (but not all) occupy whole ecological niche So; if
Mi < m < Mi+i, 1 < i < n - 1,
then populations 1, 2,n - i + 1 remain and populations n - 1, n - 2,i - 1 die out; when
Mn < M < то,
then only unique population survive and fill whole ecological niche So.
[Ackleh and Allen 2003] Ackleh A. S., Allen L. J. S. 2003. Competitive exclusion and coexistence for pathogens in an epidemic model with variable population size. J. Math. Biol. Vol.47, 153-168.
[Allen 1974] Allen P. M. 1974. "Evolution, population dynamics and stability". Proc. of the National Academy of Sciences
of the USA. Vol. 73, No 3, 665-668.
[Austin 1990] Austin M. P. 1990. Community theory and competition in vegetation . Perspectives on plant competition. San Diego: Academic Press, 215-238.
[Billik and Case 1994] Billik I., Case T. J. 1994. Higher order interactions in ecological communities: What are they and how can they be detected. . Ecology. Vol. 75, 1529-1543.
[Breder 1959] Breder C. M. 1959. Studies on social grouping in fishes. -Bull. Amer. Mus. Natur. Hist. Vol. 117. No 6,
[Caswell 2001] Caswell H. 2001. Matrix population mod-els:Constructions, Analisis, and Inerpretation. 2nd. ed. Sin-auer. Sunderland MA.
[Chernousenko et al. 1988] Chernousenko V. M., Chernenko I. V., Chernyshenko S. V. 1988. Bifurcation in the modified Eigen hypercycle . Nonlinear and turbulent processes in physics. Proc. of 3rd Intern. workshop. Kiev: Naukova
Dumka. Vol. 2, 261-263.
[Chernyshenko 1995] Chernyshenko S. V. 1995. The open Eigen Hypercycle and selforganization ofecological systems. Sustainable Development: Environmental Pollution and Ecological Safety. Dniepropetrovsk: Dniepropetrovsk Univ.
[Chernyshenko 2005] Chernyshenko S.V. 2005. Nonlinear analysis of forest ecosystems dynamics. Dnipropetrovsk, Dnipropetrovsk University Press.
[Deng 2008] Deng B. 2008. The time invariance principle, the absence ofecological chaos, and a fundamental pitfall of discrete modeling. Ecologicall Modelling. Vol.215, 287292.
[Easterling et al. 2000] Easterling M. R.,Ellner S. P., Dixon P. 2000. Size-specific sensitivity: applying a new structured population model. Ecology. Vol.81, 964-708.
[Eigen and Schuster 1979] Eigen M., Schuster P. 1979. The hy-percycle: A principle of natural selforganization. Spriger: Berlin.
[Ellner and Rees 2006] Ellner S. P., Rees M. 2006. Integral
projection models for species with complex demography. American Naturalist. Vol.167, 410-428.
[Levin 1997] Levin S. A. 1997. Models of population dispersal. Differential Equations and Applications in Ecology, Epidemics, and Population Problems. New-York: L. Academic
[Manteyfel 1992] Manteyfel B. P. 1992. Ecological and evolutional aspects of animal behaviour. Moscow: Nauka.
[Maurer 1999] Maurer B. A. 1999. Untangling ecological complexity. Chicago : Univ. of Chicago Press.
[May 1991] May R.M. 1991. Hypercycles spring to life. Nature. Vol.353, 607-609.
[Odum 1994] Odum H. T. 1994. Ecological and general systems and introduction to systems ecology. Niwot: University Press ofColorado.
[Roff1974] RoffD. A. 1974. Spatialheterogenityandpersistence of populations. Ecologia. Vol. 15, 245-258.
[Sole andBascompte 2006] Sole R.V., Bascompte J. 2006. Self-Organization in Complex Ecosystems. Monograps in Population Biology. Prinston University Press. Vol.42.
[Urich 1938] Urich I. 1938. The social hierarchy in albino mice.
J. Comp. Psychol. Vol. 25., 373-413.
[Williamson 1990] Williamson M. 1990. The analysis of biological populations. L.: Academic Press.
VASILIY Ye. BELOZYOROV was born in Dnipropetro-
vsk, Ukraine graduated from the Dnipropetrovsk State University. Obtained PhD degree on mathematical system theory in 1986. From 1996 till 2009 was, successively, head of Applied Mathematics Department at Dnipropetrovsk National University. He is an Honoured Science Worker of Ukraine. In 2010 he became a professor of Computer Technologies Department, Dnipropetrovsk National University. His e-mail address is firstname.lastname@example.org
SERGE V. CHERNYSHENKO was born in Dnipropetro-vsk, Ukraine and graduated from the Dnipropetrovsk State Uni-versity. After obtaining PhD degree on computing in 1986, was, successively, head of Laboratory of Mathematical Modeling in Biology, head of Computer Science Department, dean of Applied Mathematics Faculty at Dnipropetrovsk National University. He was a supervisor of several Ukrainian national projects on mathematical modeling. From 2009 he is a visiting professor of Koblenz-Landau University, Faculty of Informatics. His e-mail address is email@example.com and his web-site can be found at www.uni-koblenz.de/ svc.
VSEVOLOD S. CHERNYSHENKO was born in
Dnipropetrovsk, Ukraine and graduated from the Dnipropetrovsk National University. Got PhD degree on Mathematical Modeling and Numerical Methods in 2009. Nowadays he is a docent at the Computer Software Department of the National Mining University of Ukraine. He is a member of editorial board of journals "Ecology and Noospherology", "Soil Science". His e-mail address is VseVsevolod@hotmail.com and his personal webpage at
Hierarchical heterogenity of populations: modeling by the open Eigen hypercycle. V.Ye.Belozyorov, V.S. Chernyshenko, S.V. Chernyshenko. // Proceedings 26th European conference on modelling and simulation ECMS 2012, 2012, European council for modelling and simulation, Digitaldruck Pirrot GmbH, May 29 - June 01, pp. 150-156.