Cell Mapping Methods
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Cell Mapping Methods
This book presents the latest algorithmic developments in the cell-mapping method for the global analysis of nonlinear dynamic systems, global solutions for multi-objective optimization problems, and global solutions for zeros of complex algebraic equations. It also discusses related engineering and scientific applications, including the nonlinear design of structures for better vibration resistance and reliability; multi-objective, structural-acoustic design for sound abatement; optimal multi-objective design of airfoils for better lift; and optimal multi-objective design of linear and nonlinear controls with or without time delay. The first book on the subject to include extensive Matlab and C++ codes, it presents various implementation algorithms of the cell-mapping method, enabling readers to understand how the method works and its programming aspects. A link to the codes on the Springer website will be provided to the readers.
Global Nonlinear Dynamics for Engineering Design and System Safety
This is the first book which exploits concepts and tools of global nonlinear dynamics for bridging the gap between theoretical and practical stability of systems/structures, and for possibly enhancing the engineering design in macro-, micro- and nano-mechanics. Addressed topics include complementing theoretical and practical stability to achieve load carrying capacity; dynamical integrity for analyzing global dynamics, for interpreting/predicting experimental behavior, for getting hints towards engineering design; techniques for control of chaos; response of uncontrolled and controlled system/models in applied mechanics and structural dynamics by also considerung the effect of system imperfections; from relatively simple systems to multidimensional models representative of real world applications; potential and expected impact of global dynamics for engineering design.
Bifurcation and Chaos in Complex Systems
The book presents the recent achievements on bifurcation studies of nonlinear dynamical systems. The contributing authors of the book are all distinguished researchers in this interesting subject area. The first two chapters deal with the fundamental theoretical issues of bifurcation analysis in smooth and non-smooth dynamical systems. The cell mapping methods are presented for global bifurcations in stochastic and deterministic, nonlinear dynamical systems in the third chapter. The fourth chapter studies bifurcations and chaos in time-varying, parametrically excited nonlinear dynamical systems. The fifth chapter presents bifurcation analyses of modal interactions in distributed, nonlinear, dynamical systems of circular thin von Karman plates. The theories, methods and results presented in this book are of great interest to scientists and engineers in a wide range of disciplines. This book can be adopted as references for mathematicians, scientists, engineers and graduate students conducting research in nonlinear dynamical systems.· New Views for Difficult Problems· Novel Ideas and Concepts · Hilbert's 16th Problem· Normal Forms in Polynomial Hamiltonian Systems · Grazing Flow in Non-smooth Dynamical Systems· Stochastic and Fuzzy Nonlinear Dynamical Systems· Fuzzy Bifurcation· Parametrical, Nonlinear Systems· Mode Interactions in nonlinear dynamical systems