Dynamic Systems on Measure Chains: 370 - Rilegato

Lakshmikantham, V.; Kaymakcalan, B.; Sivasundaram, S.

Rilegato

ISBN 10: 0792341163 ISBN 13: 9780792341161

Casa editrice: Springer-Verlag GmbH, 1996

Riassunto

From a modelling point of view, it is realistic to model a phenomenon by a dynamic system which incorporates both continuous and discrete times, namely, time-scale or measure chain. TTherefore the question can be asked as to whether it is possible to provide a framework which permits handling of both dynamic systems simultaneously so that one can get some insight and a better understanding of the subtle differences of these two different systems. The answer is affirmative, and recently developed theory of dynamic systems on time scales offers the desired unified approach. This book presents the current state of development of the theory of dynamic systems on time scales from a qualitative point of view. It consists of four chapters. Chapter one develops systematically the necessary calculus of functions on time scales. In chapter two, we dynamic systems on time scales and prove the basic properties of solutions of such dynamic systemsare introduced. The theory of Lyapunov stability is discussed in chapter three in an appropriate setup. Chapter four is devoted to describing several different areas of investigations of dynamic systems on time scales which will provide an exciting prospect and impetus for further advances in this important area which is very new. Some important features of the work are that it demonstrates the interplay of the two different theories, namely, the theory of continuous and discrete dynamic systems, when imbedded in one unified framework and it provides an impetus to investigate in the set p of time scales other important problems which might offer a better understanding of the intricacies of a unified study.

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Contenuti

Preface. 1: 1.0. Introduction. 1.1. Measure Chains and Time Scales. 1.2. Differentiation. 1.3 Mean Value Theorem and Consequences. 1.4. Integral and Antiderivative. 1.5. Notes. 2: 2.0. Introduction. 2.1. Local Existence and Uniqueness. 2.2. Dynamic Inequalities. 2.3. Existence of Extremal Solutions. 2.4. Comparison Results. 2.5. Linear Variation of Parameters. 2.6. Continuous Dependence. 2.7. Nonlinear Variation of Parameters. 2.8. Global Existence and Stability. 2.9. Notes. 3: 3.0. Introduction. 3.1. Comparison Theorems. 3.2. Stability Criteria. 3.3. A Technique in Stability Theory. 3.4. Stability of Conditionally Invariant Sets. 3.5. Stability in Terms of Two Measures. 3.6. Vector Lyapunov Functions and Practical Stability. 3.7. Notes. 4: 4.0. Introduction. 4.1. Monotone Iterative Technique. 4.2. Method of Quasilinearization. 4.3. Monotone Flows and Stationary Points. 4.4. Invariant Manifolds. 4.5. Practical Stability of Large-Scale Uncertain Dynamic Systems. 4.6. Boundary Value Problems. 4.7. Sturmian Theory. 4.8. Convexity of Solutions Relative to the Initial Data. 4.9. Invariance Principle. 4.10. Notes. References. Subject Index.

Product Description

Book by Lakshmikantham V Sivasundaram S Kaymakcalan B

Dettagli dell'edizione

• Editore: Springer-Verlag GmbH
• Data di pubblicazione: 1996
• Lingua: Inglese
• ISBN 10: 0792341163
• ISBN 13: 9780792341161
• Rilegatura: Copertina rigida
• Numero di pagine: 308
• Contatto del produttore: non disponibile
• Persona responsabile: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Germania