Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

MathSciNet review: 1567087

Full text of review: PDF This review is available free of charge.

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.

*On the theory of stability of motion*, J. Appl. Math. Mech.

**26**(1962), 1506–1522. MR

**0150404**, DOI 10.1016/0021-8928(62)90189-2

**2.**

*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.

*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**

*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.**

*Several Lyapunov functions*, Proc. of the Fifth Internat. Conference on Nonlinear Oscillation, Kiev, U.S.S.R., 1969, pp. 268-275.

**6.**

*On the method of vector Lyapunov functions*, Proc. Twelfth Annual Allerton Conference on Circuit and System Theory, October, 1974, pp. 71-76.

*Classification of stability-like concepts and their study using vector Lyapunov functions*, J. Math. Anal. Appl.

**43**(1973), 537–570. MR

**333371**, DOI 10.1016/0022-247X(73)90090-5

**8.**

*Stability of large scale systems*, Proc. of the IFAC Fifth World Congress, 1972, pp. 1-11.

**9.**

*Competitive economic systems; stability, decomposition and aggregation*. Proc. of the IEEE Conf. on Decision and Control, 1973, pp. 265-275.

*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

*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**

*Large-scale systems: stability, complexity, reliability*, J. Franklin Inst.

**301**(1976), no. 1-2, 49–69. Recent trends in systems theory. MR

**411771**, DOI 10.1016/0016-0032(76)90132-0

*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

*Stability of model ecosystems with time-delay*, J. Theoret. Biol.

**61**(1976), no. 1, 1–13. MR

**414187**, DOI 10.1016/0022-5193(76)90099-0

*Connective stability of large-scale stochastic systems*, Internat. J. Systems Sci.

**6**(1975), no. 8, 713–721. MR

**456849**, DOI 10.1080/00207727508941855

*Stability of multispecies communities in randomly varying environment*, J. Math. Biol.

**2**(1975), no. 2, 165–178. MR

**398570**, DOI 10.1007/BF00275926

**17.**

*Stochastic stability and instability of model ecosystems*, Proc. IFAC Sixth World Congress, 1975, pp. 1-7.

**18.**

*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