Book Review
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MathSciNet review:
1567087
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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.
V. M. Matrosov, 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. 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.
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
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.
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 333371, DOI 10.1016/0022-247X(73)90090-5
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.
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
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
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 411771, DOI 10.1016/0016-0032(76)90132-0
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, 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
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 456849, DOI 10.1080/00207727508941855
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 398570, DOI 10.1007/BF00275926
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.
- 1.
- V. M. Matrosov, On the theory of stability of motion, Prikl. Mat. Meh. 26 (1962), 992-1002. 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, Symp. Math. Roma 6, Mechanica Nonlineare Stabilita 1970, Academic Press, New York (1971), 209-242. MR 280820
- 4.
- V. M. Matrosov, Comparison method in system dynamics, Differential'nye Uravnenija 10 (1974), 1547-1559; 11 (1975), 403-417. MR 374574
- 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. 44 (1973), 537-570. MR 333371
- 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.
- D. D. Siljak, Stability of large scale systems under structural perturbations, Proc. IEEE Trans, on Systems, Man and Cybernetics 3 (1972), 657-663. MR 316121
- 11.
- D. D. Siljak, Large scale dynamic systems; stability and structure, North-Holland, Amsterdam, 1977. MR 595867
- 12.
- D. D. Siljak and M. B. Vukecvie, Large scale systems: Stability complexity, reliability, J. Franklin Inst. 301 (1976), 49-69. MR 411771
- 13.
- G. S. Ladde, Cellular systems-I, Stability of chemical systems-II, Stability of compartmental systems, Math. Biosciences 29 (1976), 309-330; 30 (1976), 1-21. MR 682070
- 14.
- G. S. Ladde, Stability of model ecosystems with time-delay, J. Theoret. Biol. 61 (1976), 1-13. MR 414187
- 15.
- G. S. Ladde and D. D. Siljak, Connective stability of large scale stochastic systems, Internat. J. Systems Sci. 6 (1975), 713-721. MR 456849
- 16.
- G. S. Ladde, Stability of multispecies co-munity in ramdomly varying environment, J. Math. Biol. 2 (1975), 165-178. MR 398570
- 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