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Book Review

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Book Information:

Authors: Anthony N. Michel and Richard K. Miller
Title: Qualitative analysis of large scale dynamical systems
Additional book information: Academic Press, New York, 1977, xv + 289 pp., $22.50.

References [Enhancements On Off] (What's this?)

  • 1. V. M. Matrosov, On the theory of stability of motion, J. Appl. Math. Mech. 26 (1962), 1506–1522. MR 0150404
  • 2. V. M. Matrosov, The comparison principle with a vector valued function.I, II, and III, Differential'nye Uravnenija 4 (1968), 1374-1384, 1739-1752; 5 (1969), 1171-1185.
  • 3. V. M. Matrosov, Vector Lyapunov functions in the analysis of nonlinear interconnected systems, Symposia Mathematica, Vol. VI (INDAM, Rome, 1970) Academic Press, London, 1971, pp. 209–242. MR 0280820
  • 4. V. M. Matrosov, The comparison method in the dynamics of systems. I, II, Differencial′nye Uravnenija 10 (1974), 1547–1559, 1730; ibid. 11 (1975), 403–417, 586 (Russian). MR 0374574
  • 5. V. Lakshmikantham, Several Lyapunov functions, Proc. of the Fifth Internat. Conference on Nonlinear Oscillation, Kiev, U.S.S.R., 1969, pp. 268-275.
  • 6. V. Lakshmikantham, On the method of vector Lyapunov functions, Proc. Twelfth Annual Allerton Conference on Circuit and System Theory, October, 1974, pp. 71-76.
  • 7. P. Habets and K. Peiffer, Classification of stability-like concepts and their study using vector Lyapunov functions, J. Math. Anal. Appl. 43 (1973), 537–570. MR 0333371
  • 8. D. D. Siljak, Stability of large scale systems, Proc. of the IFAC Fifth World Congress, 1972, pp. 1-11.
  • 9. D. D. Siljak, Competitive economic systems; stability, decomposition and aggregation. Proc. of the IEEE Conf. on Decision and Control, 1973, pp. 265-275.
  • 10. Dragoslav D. Šiljak, Stability of large-scale systems under structural perturbations, IEEE Trans. Systems, Man, and Cybernet. SMC-2 (1972), 657–663. MR 0316121
  • 11. Dragoslav D. Šiljak, Large-scale dynamic systems, North-Holland Series in System Science and Engineering, vol. 3, North-Holland Publishing Co., New York-Amsterdam, 1979. Stability and structure. MR 595867
  • 12. D. D. Šiljak and M. B. Vukčević, Large-scale systems: stability, complexity, reliability, J. Franklin Inst. 301 (1976), no. 1/2, 49–69. Recent trends in systems theory. MR 0411771
  • 13. G. S. Ladde, Cellular systems. I. Stability of chemical systems, Math. Biosci. 29 (1976), no. 3-4, 309–330. MR 0682070
  • 14. G. S. Ladde, Stability of model ecosystems with time-delay, J. Theoret. Biol. 61 (1976), no. 1, 1–13. MR 0414187
  • 15. Gangaram S. Ladde and Dragoslav D. Šiljak, Connective stability of large-scale stochastic systems, Internat. J. Systems Sci. 6 (1975), no. 8, 713–721. MR 0456849
  • 16. G. S. Ladde and D. D. Šiljak, Stability of multispecies communities in randomly varying environment, J. Math. Biol. 2 (1975), no. 2, 165–178. MR 0398570
  • 17. G. S. Ladde and D. D. Siljak, Stochastic stability and instability of model ecosystems, Proc. IFAC Sixth World Congress, 1975, pp. 1-7.
  • 18. D. D. Siljak, On the stability of arms race, Chapter 9, in Mathematical Systems in International Relations Research, Edited by J. V. Gillespie and D. A. Zimmes, Praeger Publishers, New York, 1977.

Review Information:

Reviewer: V. Lakshmikantham
Journal: Bull. Amer. Math. Soc. 84 (1978), 937-939
DOI: https://doi.org/10.1090/S0002-9904-1978-14539-X