Stability of functional differential equations / V.B. Kolmanovskii and V.R. Nosov.

Format:

Book

Author/Creator:

Kolmanovskii, V. B.

Contributor:

Nosov, V. R.

Series:

Mathematics in science and engineering ; v. 180.

Mathematics in science and engineering ; v. 180

Language:

English

Subjects (All):

Functional differential equations--Numerical solutions.

Functional differential equations.

Stability.

Physical Description:

1 online resource (233 p.)

Place of Publication:

London : Academic Press, Inc., 1986.

Summary:

This book provides an introduction to the structure and stability properties of solutions of functional differential equations. Numerous examples of applications (such as feedback systrems with aftereffect, two-reflector antennae, nuclear reactors, mathematical models in immunology, viscoelastic bodies, aeroautoelastic phenomena and so on) are considered in detail. The development is illustrated by numerous figures and tables.

Contents:

Front Cover; Stability of Functional Differential Equations; Copyright Page; Contents; Preface; Chapter 1. Theoretical foundations of functional differential equations; 1. Time lags in engineering; 2. Aftereffects in physical, biological and other systems; 3. Initial-value problem for functional differential equations; 4. Linear equations; 5. Linear autonomous equations; 6. Feedback systems with aftereffects; Chapter 2. Stability of retarded equations; 1. General definitions of stability; 2. Linear autonomous retarded equations; 3. Methods of stability investigation of linear autonomous RFDEs

4. Stabilization system of the two-reflector antenna5. Liapunov direct method for equations with delay; 6. Construction of Liapunov - Krasovskii functionals; 7. Stability of nuclear reactors; 8. Mathematical models in immunology; 9. Design of adaptive controller for retarded systems; 10. Stability of viscoelastic bodies; 11. Absolute stability of systems with delay; 12. Stability of linear periodic equations; Chapter 3. Stability of neutral functional differential equations; 1. Stability of linear autonomous NFDEs; 2. Stability of aeroautoelasticity equations

3. Liapunov direct method for neutral-type equations4. Construction of degenerated functionals for concrete systems; 5. Instability of neutral-type equations; 6. Asymptotic properties of neutral-type equations; 7. Liapunov functionals depending on derivatives; 8. Stability and boundedness of linear nonhomogeneous equations; 9. Linear periodic equations; Chapter 4. Stability of stochastic functional differential equations; 1. Some prerequisites from the theory of stochastic retarded functional differential equations; 2. Formulation of stability problems for SRFDEs. Liapunov direct method

3. Stability of scalar stochastic equations4. Stability of second-order equations; 5. Stationary and periodic solutions of stochastic retarded equations; 6. Stability with respect to the first approximation; 7. Neutral-type stochastic functional differential equations; 8. Stability of linear autonomous equations; References; Index

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 202-214) and index.

ISBN:

1-282-61968-3

9786612619687

0-08-096314-5

OCLC:

700689126