Unveiling complexity: non-linear and fractal analysis in neuroscience and cognitive psychology

Tobias A Mattei

doi:10.3389/fncom.2014.00017

Abstract

Unveiling complexity: non-linear and fractal analysis in neuroscience and cognitive psychology

Highlights

Non-linear dynamics has been mastered by physicists and mathematicians for a long time, as most physical systems are inherently non-linear in nature (Kirillov and Dmitry, 2013), the more recent successful application of non-linear and fractal methods to modeling and prediction of several evolutionary, ecologic, genetic, and biochemical processes (Avilés, 1999) has generated great interest and enthusiasm for such type of approach among researchers in neuroscience and cognitive psychology
After initial works on this emerging field, it became clear that that multiple aspects of brain function as viewed from different perspectives and scales present a nonlinear behavior, with a complex phase space composed of multiple equilibrium points, limit cycles, stability regions, and trajectory flows as well as a dynamics which includes unstable periodic orbits, period-doubling bifurcations, as well as other features typical of chaotic systems (Birbaumer et al, 1995)
More recently the concept of strange attractors has lead to a new understanding of information processing in the brain which, instead of the old “localizationist” approaches (Wernicke, 1970), considers higher cognitive functions as systemic properties which emerge from the dynamic interaction between parallel streams of information flowing between highly interconnected neuronal clusters that are organized in a widely distributed circuit modulated by key central nodes (Mattei, 2013a,b)

Summary

Introduction

Non-linear dynamics has been mastered by physicists and mathematicians for a long time, as most physical systems are inherently non-linear in nature (Kirillov and Dmitry, 2013), the more recent successful application of non-linear and fractal methods to modeling and prediction of several evolutionary, ecologic, genetic, and biochemical processes (Avilés, 1999) has generated great interest and enthusiasm for such type of approach among researchers in neuroscience and cognitive psychology. After initial works on this emerging field, it became clear that that multiple aspects of brain function as viewed from different perspectives and scales present a nonlinear behavior, with a complex phase space composed of multiple equilibrium points, limit cycles, stability regions, and trajectory flows as well as a dynamics which includes unstable periodic orbits, period-doubling bifurcations, as well as other features typical of chaotic systems (Birbaumer et al, 1995).

Results

Conclusion