Competitive processes and comparison differential systems
HTML articles powered by AMS MathViewer
- by G. S. Ladde PDF
- Trans. Amer. Math. Soc. 221 (1976), 391-402 Request permission
Abstract:
Sufficient conditions are given for stability and nonnegativity of solutions of a system of differential equations, in particular, of comparison differential equations. Finally, it has been shown that the comparison differential equations represent the mathematical models for competitive processes in biological, physical and social sciences.References
- Richard Bellman, Introduction to matrix analysis, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1960. MR 0122820 —, Topics in pharmacokinetics. I: Concentration dependent rates, Math. Biosci. 6 (1970), 13-17. —, Topics in pharmacokinetics. IV: Approximation in process space and fitting by sums of exponentials, Math. Biosci. 14 (1972), 45-47. S. W. Benson, The foundations of chemical kinetics, McGraw-Hill, New York, 1960.
- Fred Brauer, Some refinements of Lyapunov’s second method, Canadian J. Math. 17 (1965), 811–819. MR 179422, DOI 10.4153/CJM-1965-079-2 H. G. Bray and K. White, Kinetics and thermodynamics in biochemistry, 2nd ed., J. & A. Churchill, London, 1966.
- R. Grimmer, Stability of a scaler differential equation, Proc. Amer. Math. Soc. 32 (1972), 452–456. MR 288369, DOI 10.1090/S0002-9939-1972-0288369-5
- Ljubomir T. Grujić and Dragoslav D. Šiljak, Asymptotic stability and instability of large-scale systems, IEEE Trans. Automatic Control AC-18 (1973), 636–645. MR 0414186, DOI 10.1109/tac.1973.1100422
- T. G. Hallam and J. W. Heidel, Structure of the solution set of some first order differential equations of comparison type, Trans. Amer. Math. Soc. 160 (1971), 501–512. MR 281995, DOI 10.1090/S0002-9947-1971-0281995-2 J. R. Hicks, Value and capital, 2nd ed., Oxford Univ. Press, Oxford, 1946.
- Lloyd A. Metzler, Stability of multiple markets: the Hicks conditions, Econometrica 13 (1945), 277–292. MR 15764, DOI 10.2307/1906922 K. K. Krasovskiĭ, Certain problems in the theory of stability of motion, Fizmatgiz, Moscow, 1959; English transl., Stability of motion. Application of Ljapunov’s second method to differential systems and equations with delay, Stanford Univ. Press, Stanford, Calif., 1963. MR 21 #5047; 26 #5258.
- G. S. Ladde, Systems of differential inequalities and stochastic differential equations. II, J. Mathematical Phys. 16 (1975), 894–900. MR 428442, DOI 10.1063/1.522594
- G. S. Ladde, Variational comparison theorem and perturbations of nonlinear systems, Proc. Amer. Math. Soc. 52 (1975), 181–187. MR 372351, DOI 10.1090/S0002-9939-1975-0372351-6 V. Lakshmikantham and S. Leela, Differential and integral inequalities, theory and applications. Vol. I, Academic Press, New York, 1969. P. K. Newman, Some notes on stability conditions, Rev. Econ. Studies 72 (1959), 1-9.
- Dragoslav D. Šiljak, Stability of large-scale systems under structural perturbations, IEEE Trans. Systems Man Cybernet. SMC-2 (1972), 657–663. MR 316121, DOI 10.1109/TSMC.1972.4309194
- D. D. Šiljak, Connective stability of competitive equilibrium, Automatica J. IFAC 11 (1975), no. 4, 389–400. MR 419034, DOI 10.1016/0005-1098(75)90088-6
- Kenneth J. Arrow and F. H. Hahn, General competitive analysis, Mathematical Economics Texts, No. 6, Holden-Day, Inc., San Francisco, Calif.; Oliver and Boyd, Edinburgh, 1971. MR 0439057
- G. S. Ladde, Cellular systems. I. Stability of chemical systems, Math. Biosci. 29 (1976), no. 3-4, 309–330. MR 682070, DOI 10.1016/0025-5564(76)90109-7
- G. S. Ladde, Cellular systems. II. Stability of compartmental systems, Math. Biosci. 30 (1976), no. 1-2, 1–21. MR 681522, DOI 10.1016/0025-5564(76)90013-4
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 221 (1976), 391-402
- MSC: Primary 34D20; Secondary 92A05, 90A99
- DOI: https://doi.org/10.1090/S0002-9947-1976-0407401-7
- MathSciNet review: 0407401