EconPapers    
Economics at your fingertips  
 

Visual Analysis of Nonlinear Dynamical Systems: Chaos, Fractals, Self-Similarity and the Limits of Prediction

Geoff Boeing

No c7p43, SocArXiv from Center for Open Science

Abstract: Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be very simple, yet they produce completely unpredictable and divergent behavior. Systems of nonlinear equations are difficult to solve analytically, and scientists have relied heavily on visual and qualitative approaches to discover and analyze the dynamics of nonlinearity. Indeed, few fields have drawn as heavily from visualization methods for their seminal innovations: from strange attractors, to bifurcation diagrams, to cobweb plots, to phase diagrams and embedding. Although the social sciences are increasingly studying these types of systems, seminal concepts remain murky or loosely adopted. This article has three aims. First, it argues for several visualization methods to critically analyze and understand the behavior of nonlinear dynamical systems. Second, it uses these visualizations to introduce the foundations of nonlinear dynamics, chaos, fractals, self-similarity and the limits of prediction. Finally, it presents Pynamical, an open-source Python package to easily visualize and explore nonlinear dynamical systems’ behavior.

Date: 2017-03-24
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2) Track citations by RSS feed

Downloads: (external link)
https://osf.io/download/58d54f3b9ad5a100455be55f/

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:osf:socarx:c7p43

DOI: 10.31219/osf.io/c7p43

Access Statistics for this paper

More papers in SocArXiv from Center for Open Science
Bibliographic data for series maintained by OSF ().

 
Page updated 2020-02-08
Handle: RePEc:osf:socarx:c7p43