Bulletin of the American Mathematical Society

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Book Information:

Author: G. St\'ep\'an
Title: Retarded dynamical systems: stability and characteristic functions
Additional book information: Longman Scientific \& Technical, Pitman Research Notes in Mathematics Series, no. 210, 1989, 151 pp; US$32.00. ISBN 0-582-03932-0.

Richard Bellman and Kenneth L. Cooke, Differential-difference equations, Academic Press, New York-London, 1963. MR 0147745

Kenneth L. Cooke and Pauline van den Driessche, On zeroes of some transcendental equations, Funkcial. Ekvac. 29 (1986), no. 1, 77–90. MR 865215

L. E. Èl′sgol′ts and S. B. Norkin, Introduction to the theory and application of differential equations with deviating arguments, Mathematics in Science and Engineering, Vol. 105, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1973. Translated from the Russian by John L. Casti. MR 0352647

Jack Hale, Theory of functional differential equations, 2nd ed., Applied Mathematical Sciences, Vol. 3, Springer-Verlag, New York-Heidelberg, 1977. MR 0508721

Brian D. Hassard, Nicholas D. Kazarinoff, and Yieh Hei Wan, Theory and applications of Hopf bifurcation, London Mathematical Society Lecture Note Series, vol. 41, Cambridge University Press, Cambridge-New York, 1981. MR 603442

V. B. Kolmanovskiĭ and V. R. Nosov, Stability of functional-differential equations, Mathematics in Science and Engineering, vol. 180, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1986. MR 860947

[7]

N. N. Krasovskiĭ, Stability of motion, Stanford Univ. Press, Stanford, CA., 1963 (translated by J. L. Brenner).

N. MacDonald, Biological delay systems: linear stability theory, Cambridge Studies in Mathematical Biology, vol. 8, Cambridge University Press, Cambridge, 1989. MR 996637

A. D. Myškis, General theory of differential equations with a retarded argument, Amer. Math. Soc. Translation 1951 (1951), no. 55, 62. MR 0046551

L. S. Pontryagin, On the zeros of some elementary transcendental functions, Amer. Math. Soc. Transl. (2) 1 (1955), 95–110. MR 0073686

Harlan W. Stech, Hopf bifurcation calculations for functional-differential equations, J. Math. Anal. Appl. 109 (1985), no. 2, 472–491. MR 802908, DOI 10.1016/0022-247X(85)90163-5

Taro Yoshizawa, Stability theory by Liapunov’s second method, Publications of the Mathematical Society of Japan, vol. 9, Mathematical Society of Japan, Tokyo, 1966. MR 0208086

[1]

R. Bellman and K. L. Cooke, Differential-difference equations, Academic Press, New York, 1963. MR 0147745 (26:5259)

[2]

K. L. Cooke and P. van den Driessche, On zeroes of some transcendental equations, Funkcialaj Ekvacioj 29 (1986), 77-90. MR 865215 (87m:34098)

[3]

L. E. El'sgol'ts and S. B. Norkin, Introduction to the theory and application of differential equations with deviating arguments, Academic Press, New York and London, 1973. MR 0352647 (50:5134)

[4]

J. K. Hale, Theory of Functional differential equations, Springer-Verlag, New York-Heidelberg-Berlin, 1977. MR 0508721 (58:22904)

[5]

B. D. Hassard, N. D. Kazarinoff, and Y. H. Wan, Theory and applications of Hopf bifurcations, London Mathematical Society Lecture Note Series no. 41, Cambridge Univ. Press, Cambridge, 1981. MR 603442 (82j:58089)

[6]

V. B. Kolmanovskiĭ and V. R. Nosov, Stability of functional differential equations, Academic Press, London and Orlando, 1986. MR 860947 (88e:34001)

[7]

N. N. Krasovskiĭ, Stability of motion, Stanford Univ. Press, Stanford, CA., 1963 (translated by J. L. Brenner).

[8]

N. MacDonald, Biological delay system: linear stability theory, Cambridge Univ. Press, Cambridge, 1989. MR 996637 (90h:92020)

[9]

A. D. Myshkis, General theory of differential equations with delay, Amer. Math. Soc. Transl. 55 (1951), 1-62. MR 0046551 (13:752a)

[10]

L. S. Pontrjagin, On the zeros of some elementary transcendental functions, Amer. Math. Soc. Transl., (2) 1 (1955), 95-110. MR 0073686 (17:471c)

[11]

H. W. Stech, Hopf bifurcation calculations for functional differential equations, J. Math. Anal. Appl. 109 (1985), 472-491. MR 802908 (87h:58165)

[12 T]

Yoshizawa, Stability theory by Liapunov's second method, Publications of the Mathematical Society of Japan, no. 9, Tokyo, 1966. MR 0208086 (34:7896)