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Nonlinear systems with random structures arise quite frequently as mathematical models in diverse disciplines. This monograph presents a systematic treatment of stability theory and the theory of stabilization of nonlinear systems with random structure in terms of new developments in the direct Lyapunov's method. The analysis focuses on dynamic sys
This book deals with the class of singular systems with random abrupt changes also known as singular Markovian jump systems. Various problems and their robustness are tackled. The book examines both the theoretical and practical aspects of the control problems from the angle of the structural properties of linear systems. It can be used as a textbook as well as a reference for researchers in control or mathematics with interest in control theory.
Establishing a new concept of local Lyapunov exponents the author brings together two separate theories, namely Lyapunov exponents and the theory of large deviations. Specifically, a linear differential system is considered which is controlled by a stochastic process that during a suitable noise-intensity-dependent time is trapped near one of its so-called metastable states. The local Lyapunov exponent is then introduced as the exponential growth rate of the linear system on this time scale. Unlike classical Lyapunov exponents, which involve a limit as time increases to infinity in a fixed system, here the system itself changes as the noise intensity converges, too.
The 11th International Workshop on Dynamics and Control brought together scientists and engineers from diverse fields and gave them a venue to develop a greater understanding of this discipline and how it relates to many areas in science, engineering, economics, and biology. The event gave researchers an opportunity to investigate ideas and techniq
Asymptotic Methods in Resonance Analytical Dynamics presents new asymptotic methods for the analysis and construction of solutions (mainly periodic and quasiperiodic) of differential equations with small parameters. Along with some background material and theory behind these methods, the authors also consider a variety of problems and applications in nonlinear mechanics and oscillation theory. The methods examined are based on two types: the generalized averaging technique of Krylov-Bogolubov and the numeric-analytical iterations of Lyapunov-Poincaré. This text provides a useful source of reference for postgraduates and researchers working in this area of applied mathematics.
Students and researchers in applied mathematics and applied economics can use this introductory-level graduate text. It looks at the current problems of the development of the global economy by studying the dynamics of key economic variables, such as gross national product, interest rates, employment, value of capital stock, prices (inflation) and balance of payments. Validation of the model is attempted using the economic time series of several countries. The constructed models explain the macroeconomic data of nations as dynamic games of pursuit, which are equivalent to "control" problems and are used to study mathematical optimal control of the growth of the wealth of nations. This invaluable reference for graduates and researchers compares the extent of government intervention in the economy with private firms to ensure the controllability of the economy.
A major step in differential games is determining an explicit form of the strategies of players who follow a certain optimality principle. To do this, the associated modification of Bellman dynamic programming problems has to be solved; for some differential games this could be Lyapunov functions whose "arsenal" has been supplied by stability theor
The book discusses set-valued differential equations defined in terms of the Hukuhara derivative. Focusing on equations with uncertainty, i.e., including an unknown parameter, it introduces a regularlization method to handle them. The main tools for qualitative analysis are the principle of comparison of Chaplygin – Wazhewsky, developed for the scalar, vector and matrix-valued Lyapunov functions and the method of nonlinear integral inequalities, which are used to establish existence, stability or boundedness. Driven by the question of how to model real processes using a set-valued of differential equations, the book lays the theoretical foundations for further study in this area. It is intended for experts working in the field of qualitative analysis of differential and other types of equations.
This monograph presents recent developments in spectral conditions for the existence of periodic and almost periodic solutions of inhomogenous equations in Banach Spaces. Many of the results represent significant advances in this area. In particular, the authors systematically present a new approach based on the so-called evolution semigroups with an original decomposition technique. The book also extends classical techniques, such as fixed points and stability methods, to abstract functional differential equations with applications to partial functional differential equations. Almost Periodic Solutions of Differential Equations in Banach Spaces will appeal to anyone working in mathematical analysis.
Volume 1: Deterministic Modeling, Methods and Analysis For more than half a century, stochastic calculus and stochastic differential equations have played a major role in analyzing the dynamic phenomena in the biological and physical sciences, as well as engineering. The advancement of knowledge in stochastic differential equations is spreading rapidly across the graduate and postgraduate programs in universities around the globe. This will be the first available book that can be used in any undergraduate/graduate stochastic modeling/applied mathematics courses and that can be used by an interdisciplinary researcher with a minimal academic background. An Introduction to Differential Equations: Volume 2 is a stochastic version of Volume 1 (“An Introduction to Differential Equations: Deterministic Modeling, Methods and Analysis”). Both books have a similar design, but naturally, differ by calculi. Again, both volumes use an innovative style in the presentation of the topics, methods and concepts with adequate preparation in deterministic Calculus. Errata Errata (32 KB)