Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2008-11-05
Nonlinear Sciences
Adaptation and Self-Organizing Systems
51 Pages, 14 Figures
Scientific paper
This paper draws distinctions among various concepts related to tipping points, robustness, path dependence, and other properties of system dynamics. For each concept a formal definition is provided that utilizes Markov model representations of systems. We start with the basic features of Markov models and definitions of the foundational concepts of system dynamics. Then various tipping point-related concepts are described, defined, and illustrated with a simplified graphical example in the form of a stylized state transition diagram. The tipping point definitions are then used as a springboard to describe, formally define, and illustrate many distinct concepts collectively referred to as "robustness". The final definitional section explores concepts of path sensitivity and how they can be revealed in Markov models. The definitions provided are presented using probability theory; in addition, each measure has an associated algorithm using matrix operations (excluded from current draft). Finally an extensive future work section indicates many directions this research can branch into and which methodological, conceptual, and practical benefits can be realized through this suite of techniques.
No associations
LandOfFree
Measures of Tipping Points, Robustness, and Path Dependence does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Measures of Tipping Points, Robustness, and Path Dependence, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Measures of Tipping Points, Robustness, and Path Dependence will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-372871