Dynamics of Macrosystems: Proceedings of a Workshop on the by Elie Bienenstock (auth.), Prof. Dr. Jean-Pierre Aubin, Prof.

By Elie Bienenstock (auth.), Prof. Dr. Jean-Pierre Aubin, Prof. Dr. Donald Saari, Prof. Dr. Karl Sigmund (eds.)

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Read Online or Download Dynamics of Macrosystems: Proceedings of a Workshop on the Dynamics of Macrosystems Held at the International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria, September 3–7, 1984 PDF

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Extra info for Dynamics of Macrosystems: Proceedings of a Workshop on the Dynamics of Macrosystems Held at the International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria, September 3–7, 1984

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C. (1979). Mathematical Aspects of Reacting and Diffusing Systems. Springer-Verlag, Berlin. Hofbauer, J. (1981) General cooperati6n theorem for hypercycles. Monatsh. Math. 91: 233-240. 48 Hutson, V. and Moran, W. (1982). Persistence of species obeying difference equations. J. Hath. BioI. 15: 203-213. T. (1983a). On a criterion for survival of species in models governed by difference equations. J. Math. BioI. 18: 89-90. T. (1983b). A criterion for permanent coexistence of species, with an application to a two-prey one-predator system.

Hence the inequality follows by monotonicity. (c) Let the function f = f(s) be defined by x+y x+y f ( s) = log t( 2 +s,~-s) . 0, lim f~s) = 1/2 and s~ we get 0 < f' (s) < 1/2 for all s E Since f' (0) o < = (~-~) ax dy log t(x,y) (d) For the function f f(s) > flO) < 1/2 f"(s) (O,~) > 0 for all s E R, and hence for all (x,y) E R2 with x > y. f(s) defined in (c), we get for all s E R, which implies the left-hand inequality in (d). To prove the right-hand inequality, define the function g(s) = log t(2~+Y+s,2X;Y_2S).

Contribution il l'~tude de syst~mes dissipatifs chimiques: r~actions oscillantes de Briggs-Rauscher et de Belousov-Zhabotinskii. Thesis, University of Bordeaux I. 1978. M. Lasry. Un syst~me parabolique produisant des solitons. hier de Math. de La lJdcision. 8203. CI~REMADE. University of Paris-Dauphine. 1982 (see also [8}). 39 6. M. Lasry. Sur les syst~mes parabolique produisant des solitons. Proceedtngs of the 4th seminar of the School of 'Iheoretical Biology {4-6 June 1964}. Forthcoming. 9. L.

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