Bücher der Reihe Nonlinear Physical Science

This book discusses some scaling properties and characterizes two-phase transitions for chaotic dynamics in nonlinear systems described by mappings. The chaotic dynamics is determined by the unpredictability of the time evolution of two very close initial conditions in the phase space. It yields in an exponential divergence from each other as time passes. The chaotic diffusion is investigated, leading to a scaling invariance, a characteristic of a continuous phase transition. Two different types of transitions are considered in the book. One of them considers a transition from integrability to non-integrability observed in a two-dimensional, nonlinear, and area-preserving mapping, hence a conservative dynamics, in the variables action and angle. The other transition considers too the dynamics given by the use of nonlinear mappings and describes a suppression of the unlimited chaotic diffusion for a dissipative standard mapping and an equivalent transition in the suppression of Fermi acceleration in time-dependent billiards. This book allows the readers to understand some of the applicability of scaling theory to phase transitions and other critical dynamics commonly observed in nonlinear systems. That includes a transition from integrability to non-integrability and a transition from limited to unlimited diffusion, and that may also be applied to diffusion in energy, hence in Fermi acceleration. The latter is a hot topic investigated in billiard dynamics that led to many important publications in the last few years. It is a good reference book for senior- or graduate-level students or researchers in dynamical systems and control engineering, mathematics, physics, mechanical and electrical engineering.

This book explores recent developments in theoretical research and mathematical modelling of real-world complex systems, organized in four parts.  The first part of the book is devoted to the mathematical tools for the design and analysis in engineering and social science study cases. We discuss the periodic evolutions in nonlinear chemical processes, vibro-compact systems and their behaviour, different types of metal-semiconductor self-assembled samples, made of silver nanowires and zinc oxide nanorods.The second part of the book is devoted to mathematical description and modelling of the critical events, climate change and robust emergency scales. In three chapters, we consider a climate-economy model with endogenous carbon intensity and the behaviour of Tehran Stock Exchange market under international sanctions.The third part of the book is devoted to fractional dynamic and fractional control problems. We discuss the novel operational matrix technique for variable-order fractional optimal control problems, the nonlinear variable-order time fractional convection-diffusion equation with generalized polynomialsThe fourth part of the book concerns solvability and inverse problems in differential and integro-differential equations.The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering. It can be read by mathematicians, physicists, complex systems scientists, IT specialists, civil engineers, data scientists and urban planners.

This book explores recent developments in theoretical research and data analysis of real-world complex systems, organized in three parts, namelyEntropy, information, and complexity functionsMultistability, oscillations, and rhythmic synchronizationDiffusions, rotation, and convection in fluids The collection of works devoted to the memory of Professor Valentin Afraimovich provides a deep insight into the recent developments in complexity science by introducing new concepts, methods, and applications in nonlinear dynamical systems covering physical problems and mathematical modelling relevant to economics, genetics, engineering vibrations, as well as classic problems in physics, fluid and climate dynamics, and urban dynamics. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering. It can be read by mathematicians, physicists, complex systems scientists, IT specialists, civil engineers, data scientists, and urban planners.

This book demonstrates how mathematical methods and techniques can be used in synergy and create a new way of looking at complex systems.

This book is about Lie group analysis of differential equations for physical and engineering problems. The topics include:-- Approximate symmetry in nonlinear physical problems-- Complex methods for Lie symmetry analysis-- Lie group classi¿cation, Symmetry analysis, and conservation laws -- Conservative difference schemes-- Hamiltonian structure and conservation laws of three-dimensional linear elasticity-- Involutive systems of partial differential equations This collection of works is written in memory of Professor Nail H. Ibragimov (1939¿2018). It could be used as a reference book in differential equations in mathematics, mechanical, and electrical engineering.

This book demonstrates how mathematical methods and techniques can be used in synergy and create a new way of looking at complex systems.

This book is the first to present the application of the hybrid system theory to systems with EPCA (equations with piecewise continuous arguments).

This book focuses on a particular domain of Type-2 Fuzzy Logic, related to process modeling and control applications. It deepens readers'understanding of Type-2 Fuzzy Logic with regard to the following three topics: using simpler methods to train a Type-2 Takagi-Sugeno Fuzzy Model;

This book provides students and researchers with a systematic solution for fluid-induced structural vibrations, galloping instability and the chaos of cables. They will also gain a better understanding of stable and unstable periodic motions and chaos in fluid-induced structural vibrations.

This book focuses on bifurcation theory for autonomous and nonautonomous differential equations with discontinuities of different types - those with jumps present either in the right-hand side, or in trajectories or in the arguments of solutions of equations.

This book presents detailed descriptions of chaos for continuous-time systems. It is the first-ever book to consider chaos as an input for differential and hybrid equations. The findings strongly suggest that chaos theory can proceed from the theory of differential equations to a higher level than previously thought.

This unique book presents the discretization of continuous systems and implicit mapping dynamics of periodic motions to chaos in continuous nonlinear systems.

"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book.