Abstract
Here are special simple cases of MM of ES and examples of analytic solutions, The conditions for existence and uniqueness of solutions for the systems of equations and also stability of solutions are established. Some cases of non-uniqueness of solutions are considered. Cases of oscillating and wave solutions are found. Asymptotic properties of solutions are investigated.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Baker C. T. H., The Numerical Treatment of Integral Equations, Clarendon, 1977, 1034 pp.
Caratheodory C., Gesammelte Mathematische Schriften, Munhen, 1954–1957, Rd. 1–5.
Girlin S.K., Modeling of Originating Evolutionary Systems, Dokl. AN Ukr. SSR, 1987, 65–67 (in Russian).
Gluskov V.M., Ivanov V.V., Yatsenko Yu.P., Analytical Investigation of One Class of Dynamic Models, I, Cybernetics, Plenum Publish. Corp., 16, N 2, 1980, 164–177.
Korn G.A., Korn T.M., Mathematical Handbook for Scientists and Engineers, McGraw-Hill Book, 1968, 1130 pp.
Maizec C.J., Spiegel E.A., Ordinary Differential Equations with Strange Attractors, SIAM J. Appl. Math., 38, N 3, 1980, 403–421.
May R.M., Necessity and Chance: Deterministic Chaos in Ecology and Evolution, Bulletin (New Series) of the AMS, Vol. 32, N. 3, 1995, 291–308.
Murray J.D., Asymptotic Analysis, Springer, 1992, 180 pp.
Standard Mathematical Tables and Formulae, CRC Press, 1995,612 pp.
Vuginshtein A.E., Ivanov V.V., Analytic Investigation of Continuous Models of Developing Systems, Soviet Math. Dokl., 273 (2), 1984, 600–604.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Ivanov, V.V. (1999). Investigation of Equations. In: Model Development and Optimization. Applied Optimization, vol 28. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4062-5_3
Download citation
DOI: https://doi.org/10.1007/978-1-4615-4062-5_3
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6819-9
Online ISBN: 978-1-4615-4062-5
eBook Packages: Springer Book Archive