Dynamics Nonlinear

Written when the young science of chaos was gaining a foothold in the scientific community, this book introduces the field's concepts, applications, theory, and technique. Suitable for advanced underg

Using phase–plane analysis, findings from the theory of topological horseshoes and linked-twist maps, this book presents a novel method to prove the existence of chaotic dynamics. In dynamical systems

Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engin

Presenting a systematic model reduction and hierarchical controller design framework for broad classes of integrated process systems encountered in practice, this book first studies process systems with large material recycle and/or with small purge streams, followed by systems with energy integration. Step-by-step model reduction procedures are developed to derive nonlinear reduced models of the dynamics in each time scale. Hierarchical control architectures consisting of coordinated levels of control action in different time scales are proposed for each class of process systems considered to enforce stability, tracking performance and disturbance rejection. Numerous process applications are discussed in detail to illustrate the application of the methods and their potential to improve process operations. MATLAB codes are also presented to guide further application of the methods developed and facilitate practical implementations.

This work considers a small random perturbation of alpha-stable jump type nonlinear reaction-diffusion equations with Dirichlet boundary conditions over an interval. It has two stable points whose dom

The growing impact of nonlinear science on biology and medicine is fundamentally changing our view of living organisms and disease processes. This book introduces the application to biomedicine of a broad range of interdisciplinary concepts from nonlinear dynamics, such as self-organization, complexity, coherence, stochastic resonance, fractals and chaos. It comprises 18 chapters written by leading figures in the field and covers experimental and theoretical research, as well as the emerging technological possibilities such as nonlinear control techniques for treating pathological biodynamics, including heart arrhythmias and epilepsy. This book will attract the interest of professionals and students from a wide range of disciplines, including physicists, chemists, biologists, sensory physiologists and medical researchers such as cardiologists, neurologists and biomedical engineers.