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Handbook of Differential Equations: Ordinary Differential Equations
This handbook is the fourth volume in a series of volumes devoted to self-contained and up-to-date surveys in the theory of ordinary differential equations, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience. - Covers a variety of problems in ordinary differential equations - Pure mathematical and real-world applications - Written for mathematicians and scientists of many related fields
Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems
Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems is devoted to the study of bifurcations of periodic solutions for general n-dimensional discontinuous systems. The authors study these systems under assumptions of transversal intersections with discontinuity-switching boundaries. Furthermore, bifurcations of periodic sliding solutions are studied from sliding periodic solutions of unperturbed discontinuous equations, and bifurcations of forced periodic solutions are also investigated for impact systems from single periodic solutions of unperturbed impact equations. In addition, the book presents studies for weakly coupled discontinuous systems, and also the local asymptotic propert...
Iterative Learning Control for Equations with Fractional Derivatives and Impulses
This book introduces iterative learning control (ILC) and its applications to the new equations such as fractional order equations, impulsive equations, delay equations, and multi-agent systems, which have not been presented in other books on conventional fields. ILC is an important branch of intelligent control, which is applicable to robotics, process control, and biological systems. The fractional version of ILC updating laws and formation control are presented in this book. ILC design for impulsive equations and inclusions are also established. The broad variety of achieved results with rigorous proofs and many numerical examples make this book unique. This book is useful for graduate students studying ILC involving fractional derivatives and impulsive conditions as well as for researchers working in pure and applied mathematics, physics, mechanics, engineering, biology, and related disciplines.
Bifurcation and Chaos in Discontinuous and Continuous Systems
"Bifurcation and Chaos in Discontinuous and Continuous Systems" provides rigorous mathematical functional-analytical tools for handling chaotic bifurcations along with precise and complete proofs together with concrete applications presented by many stimulating and illustrating examples. A broad variety of nonlinear problems are studied involving difference equations, ordinary and partial differential equations, differential equations with impulses, piecewise smooth differential equations, differential and difference inclusions, and differential equations on infinite lattices as well. This book is intended for mathematicians, physicists, theoretically inclined engineers and postgraduate stud...
Topological Degree Approach to Bifurcation Problems
1. 1 Preface Many phenomena from physics, biology, chemistry and economics are modeled by di?erential equations with parameters. When a nonlinear equation is est- lished, its behavior/dynamics should be understood. In general, it is impossible to ?nd a complete dynamics of a nonlinear di?erential equation. Hence at least, either periodic or irregular/chaotic solutions are tried to be shown. So a pr- erty of a desired solution of a nonlinear equation is given as a parameterized boundary value problem. Consequently, the task is transformed to a solvability of an abstract nonlinear equation with parameters on a certain functional space. When a family of solutions of the abstract equation is kno...
Stability and Controls Analysis for Delay Systems
Stability and Controls Analysis for Delay Systems is devoted to stability, controllability and iterative learning control (ILC) to delay systems, including first order system, oscillating systems, impulsive systems, fractional systems, difference systems and stochastic systems raised from physics, biology, population dynamics, ecology and economics, currently not presented in other books on conventional fields. Delayed exponential matrix function approach is widely used to derive the representation and stability of the solutions and the controllability. ILC design are also established, which can be regarded as a way to find the control function. The broad variety of achieved results with rigorous proofs and many numerical examples make this book unique. - Presents the representation and stability of solutions via the delayed exponential matrix function approach - Gives useful sufficient conditions to guarantee controllability - Establishes ILC design and focuses on new systems such as the first order system, oscillating systems, impulsive systems, fractional systems, difference systems and stochastic systems raised from various subjects
Fractional-Order Equations and Inclusions
This book presents fractional difference, integral, differential, evolution equations and inclusions, and discusses existence and asymptotic behavior of their solutions. Controllability and relaxed control results are obtained. Combining rigorous deduction with abundant examples, it is of interest to nonlinear science researchers using fractional equations as a tool, and physicists, mechanics researchers and engineers studying relevant topics. Contents Fractional Difference Equations Fractional Integral Equations Fractional Differential Equations Fractional Evolution Equations: Continued Fractional Differential Inclusions
Fractional Hermite-Hadamard Inequalities
This book extends classical Hermite-Hadamard type inequalities to the fractional case via establishing fractional integral identities, and discusses Riemann-Liouville and Hadamard integrals, respectively, by various convex functions. Illustrating theoretical results via applications in special means of real numbers, it is an essential reference for applied mathematicians and engineers working with fractional calculus. Contents Introduction Preliminaries Fractional integral identities Hermite-Hadamard inequalities involving Riemann-Liouville fractional integrals Hermite-Hadamard inequalities involving Hadamard fractional integrals
Modeling, Analysis And Control Of Dynamical Systems With Friction And Impacts
This book is aimed primarily towards physicists and mechanical engineers specializing in modeling, analysis, and control of discontinuous systems with friction and impacts. It fills a gap in the existing literature by offering an original contribution to the field of discontinuous mechanical systems based on mathematical and numerical modeling as well as the control of such systems. Each chapter provides the reader with both the theoretical background and results of verified and useful computations, including solutions of the problems of modeling and application of friction laws in numerical computations, results from finding and analyzing impact solutions, the analysis and control of dynamical systems with discontinuities, etc. The contents offer a smooth correspondence between science and engineering and will allow the reader to discover new ideas. Also emphasized is the unity of diverse branches of physics and mathematics towards understanding complex piecewise-smooth dynamical systems. Mathematical models presented will be important in numerical experiments, experimental measurements, and optimization problems found in applied mechanics.
Non-Instantaneous Impulsive Differential Equations: Basic Theory and Computation
Non-instantaneous impulsive differential equations are widely used in physics, biology, dynamics and ecology and have a wide-ranging scope within the scientific industry. This book will help pave the way for a better fundamental understanding of the mathematical models and how they can be implemented.
