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.
 1.
V.
M. Matrosov, On the theory of stability of motion, J. Appl.
Math. Mech. 26 (1962), 1506–1522. MR 0150404
(27 #403)
 2.
V. M. Matrosov, The comparison principle with a vector valued function.I, II, and III, Differential'nye Uravnenija 4 (1968), 13741384, 17391752; 5 (1969), 11711185.
 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
(43 #6539)
 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
(51 #10774)
 5.
V. Lakshmikantham, Several Lyapunov functions, Proc. of the Fifth Internat. Conference on Nonlinear Oscillation, Kiev, U.S.S.R., 1969, pp. 268275.
 6.
V. Lakshmikantham, On the method of vector Lyapunov functions, Proc. Twelfth Annual Allerton Conference on Circuit and System Theory, October, 1974, pp. 7176.
 7.
P.
Habets and K.
Peiffer, Classification of stabilitylike concepts and their study
using vector Lyapunov functions, J. Math. Anal. Appl.
43 (1973), 537–570. MR 0333371
(48 #11696)
 8.
D. D. Siljak, Stability of large scale systems, Proc. of the IFAC Fifth World Congress, 1972, pp. 111.
 9.
D. D. Siljak, Competitive economic systems; stability, decomposition and aggregation. Proc. of the IEEE Conf. on Decision and Control, 1973, pp. 265275.
 10.
Dragoslav
D. Šiljak, Stability of largescale systems under structural
perturbations, IEEE Trans. Systems, Man, and Cybernet.
SMC2 (1972), 657–663. MR 0316121
(47 #4669)
 11.
Dragoslav
D. Šiljak, Largescale dynamic systems, NorthHolland
Series in System Science and Engineering, vol. 3, NorthHolland
Publishing Co., New YorkAmsterdam, 1979. Stability and structure. MR 595867
(82j:93004)
 12.
D.
D. Šiljak and M.
B. Vukčević, Largescale systems: stability,
complexity, reliability, J. Franklin Inst. 301
(1976), no. 1/2, 49–69. Recent trends in systems theory. MR 0411771
(53 #15499)
 13.
G.
S. Ladde, Cellular systems. I. Stability of chemical systems,
Math. Biosci. 29 (1976), no. 34, 309–330. MR 0682070
(58 #33092)
 14.
G.
S. Ladde, Stability of model ecosystems with timedelay, J.
Theoret. Biol. 61 (1976), no. 1, 1–13. MR 0414187
(54 #2291)
 15.
Gangaram
S. Ladde and Dragoslav
D. Šiljak, Connective stability of largescale stochastic
systems, Internat. J. Systems Sci. 6 (1975),
no. 8, 713–721. MR 0456849
(56 #15069)
 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
(53 #2421)
 17.
G. S. Ladde and D. D. Siljak, Stochastic stability and instability of model ecosystems, Proc. IFAC Sixth World Congress, 1975, pp. 17.
 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.
 1.
 V. M. Matrosov, On the theory of stability of motion, Prikl. Mat. Meh. 26 (1962), 9921002. MR 150404
 2.
 V. M. Matrosov, The comparison principle with a vector valued function.I, II, and III, Differential'nye Uravnenija 4 (1968), 13741384, 17391752; 5 (1969), 11711185.
 3.
 V. M. Matrosov, Vector Lyapunov functions in the analysis of nonlinear interconnected systems, Symp. Math. Roma 6, Mechanica Nonlineare Stabilita 1970, Academic Press, New York (1971), 209242. MR 280820
 4.
 V. M. Matrosov, Comparison method in system dynamics, Differential'nye Uravnenija 10 (1974), 15471559; 11 (1975), 403417. MR 374574
 5.
 V. Lakshmikantham, Several Lyapunov functions, Proc. of the Fifth Internat. Conference on Nonlinear Oscillation, Kiev, U.S.S.R., 1969, pp. 268275.
 6.
 V. Lakshmikantham, On the method of vector Lyapunov functions, Proc. Twelfth Annual Allerton Conference on Circuit and System Theory, October, 1974, pp. 7176.
 7.
 P. Habets and K. Peiffer, Classification of stability like concepts and their study using vector Lyapunov functions, J. Math. Anal. Appl. 44 (1973), 537570. MR 333371
 8.
 D. D. Siljak, Stability of large scale systems, Proc. of the IFAC Fifth World Congress, 1972, pp. 111.
 9.
 D. D. Siljak, Competitive economic systems; stability, decomposition and aggregation. Proc. of the IEEE Conf. on Decision and Control, 1973, pp. 265275.
 10.
 D. D. Siljak, Stability of large scale systems under structural perturbations, Proc. IEEE Trans, on Systems, Man and Cybernetics 3 (1972), 657663. MR 316121
 11.
 D. D. Siljak, Large scale dynamic systems; stability and structure, NorthHolland, Amsterdam, 1977. MR 595867
 12.
 D. D. Siljak and M. B. Vukecvie, Large scale systems: Stability complexity, reliability, J. Franklin Inst. 301 (1976), 4969. MR 411771
 13.
 G. S. Ladde, Cellular systemsI, Stability of chemical systemsII, Stability of compartmental systems, Math. Biosciences 29 (1976), 309330; 30 (1976), 121. MR 682070
 14.
 G. S. Ladde, Stability of model ecosystems with timedelay, J. Theoret. Biol. 61 (1976), 113. MR 414187
 15.
 G. S. Ladde and D. D. Siljak, Connective stability of large scale stochastic systems, Internat. J. Systems Sci. 6 (1975), 713721. MR 456849
 16.
 G. S. Ladde, Stability of multispecies comunity in ramdomly varying environment, J. Math. Biol. 2 (1975), 165178. MR 398570
 17.
 G. S. Ladde and D. D. Siljak, Stochastic stability and instability of model ecosystems, Proc. IFAC Sixth World Congress, 1975, pp. 17.
 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), 937939
DOI:
http://dx.doi.org/10.1090/S00029904197814539X
PII:
S 00029904(1978)14539X
