The architecture and learning procedure underlying ANFIS (adaptive-network-based fuzzy inference system) is presented, which is a fuzzy inference system implemented in the framework of adaptive networks. By using a hybrid learning procedure, the proposed ANFIS can construct an input-output mapping based on both human knowledge (in the form of fuzzy if-then rules) and stipulated input-output data pairs. In the simulation, the ANFIS architecture is employed to model nonlinear functions, identify nonlinear components on-line in a control system, and predict a chaotic time series, all yielding remarkable results. Comparisons with artificial neural networks and earlier work on fuzzy modeling are listed and discussed. Other extensions of the proposed ANFIS and promising applications to automatic control and signal processing are also suggested. >

ANFIS: adaptive-network-based fuzzy inference system

New developments in the science of learning science of learning overview mind and brain how experts differ from novices how children learn learning and transfer the learning environment curriculum, instruction and commnity effective teaching - examples in history, mathematics and science teacher learning technology to support learning conclusions from new developments in the science of learning.

How people learn: Brain, mind, experience, and school.

—The newly inaugurated Research Resource for Complex Physiologic Signals, which was created under the auspices of the National Center for Research Resources of the National Institutes of He...

http://ecg.mit.edu/george/publications/physionet-circ-2000.pdf

PhysioBank, PhysioToolkit, and PhysioNet: components of a new research resource for complex physiologic signals.

/pdf/determining-lyapunov-exponents-from-a-time-series-3bxxq6d0wt.pdf

Determining Lyapunov exponents from a time series

https://www.tau.ac.il/%7Eklafter1/258.pdf

The random walk's guide to anomalous diffusion: a fractional dynamics approach

First-order nonlinear differential-delay equations describing physiological control systems are studied. The equations display a broad diversity of dynamical behavior including limit cycle oscillations, with a variety of wave forms, and apparently aperiodic or "chaotic" solutions. These results are discussed in relation to dynamical respiratory and hematopoietic diseases.

https://science.sciencemag.org/content/sci/197/4300/287.full.pdf

Oscillation and Chaos in Physiological Control Systems

In an important new contribution to the literature of chaos, two distinguished researchers in the field of physiology probe central theoretical questions about physiological rhythms. Topics discussed include: How are rhythms generated? How do they start and stop? What are the effects of perturbation of the rhythms? How are oscillations organized in space? Leon Glass and Michael Mackey address an audience of biological scientists, physicians, physical scientists, and mathematicians, but the work assumes no knowledge of advanced mathematics. Variation of rhythms outside normal limits, or appearance of new rhythms where none existed previously, are associated with disease. One of the most interesting features of the book is that it makes a start at explaining "dynamical diseases" that are not the result of infection by pathogens but that stem from abnormalities in the timing of essential functions. From Clocks to Chaos provides a firm foundation for understanding dynamic processes in physiology.

From Clocks to Chaos: The Rhythms of Life

Chaos, Fractals, and Noise

This is a treatment of a variety of mathematical systems generating densities, ranging from one-dimensional discrete time transformations through continuous time systems described by integro-partial differential equations. Examples have been drawn from a variety of the sciences to illustrate the utility of the techniques presented. This material was organized and written to be accessible to scientists with knowledge of advanced calculus and differential equations. The past few years have witnessed an explosive growth in interest in physical, biological and economic systems that could be profitably studied using densities. Due to the general inaccessibility of the mathematical literature to the non-mathematician, there has been little diffusion of the concepts and techniques from ergodic theory into the study of these "chaotic" systems. This book intends to bridge that gap.

Michael C. Mackey

Papers

Oscillation and Chaos in Physiological Control Systems

From Clocks to Chaos: The Rhythms of Life

Chaos, Fractals, and Noise

Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics

From clocks to chaos