This book provides a compilation of mathematical-computational tools that are used to analyze experimental data. The techniques presented are those that have been most widely and successfully applied to the analysis of physiological systems, and address issues such as randomness, determinism, dimension, and nonlinearity. In addition to bringing together the most useful methods, sufficient mathematical background is provided to enable non-specialists to understand and apply the computational techniques. Thus, the material will be useful to life-science investigators on several levels, from physiologists to bioengineer.

Initial chapters present background material on dynamic systems, statistics, and linear system analysis. Each computational technique is demonstrated with examples drawn from physiology, and several chapters present case studies from oculomotor control, neuroscience, cardiology, psychology, and epidemiology. Throughout the text, historical notes give a sense of the development of the field and provide a perspective on how the techniques were developed and where they might lead. The overall approach is based largely on the analysis of trajectories in the state space, with emphasis on time-delay reconstruction of state-space trajectories. The goal of the book is to enable readers to apply these methods to their own research.

Contents:

• The Mathematical Analysis of Physiological Systems: Goals and Approaches
• Fundamental Signal Processing and Analysis Concepts and Measures
• Analysis Approaches Based on Linear Systems
• State-Space Reconstruction
• Dimensions
• Surrogate Data
• Nonlinear Forecasting
• Recurrence Analysis
• Tests for Dynamical Interdependence
• Unstable Periodic Orbits
• Other Approaches Based on the State Space
• Poincaré Sections, Fixed Points, and Control of Chaotic Systems
• Stochastic Measures Related to Nonlinear Dynamical Concepts
• From Measurements to Models
• Case Study — Oculomotor Control
• Case Study — Motor Control
• Case Study — Neurological Tremor
• Case Study — Neural Dynamics and Epilepsy
• Case Study — Cardiac Dynamics and Fibrillation
• Case Study — Epidemiology
• Case Study — Psychology

“Most chapters discuss early apparent success in detecting signs of low-dimensional nonlinear dynamics, but follow up with more careful studies which throw doubt on earlier findings.”