Nonlinear Dynamical Systems Workshop 2024

Nonlinear Dynamical Systems Workshop (July 15-19)

Do you...

  • Have data that you think could yield more insight if only you knew the right way to analyze it?

  • Want to ask different questions in your research, but don’t know the techniques to answer those questions?

  • Want to explore your data in ways that are less reductive, but don’t know how to do that?

  • Need to explain to a reviewer or review committee that a non-traditional approach is appropriate for your research?

If you answered “yes” to any of those questions, then this workshop is what you are looking for!

 

Nonlinear dynamical systems

Nonlinear dynamical systems (NDS) studies how systems change by searching for how the system state (a collection of variables that describe the system) is related to the state at past times. The study of NDS “significantly enriches [your] capability to conceptualize change, and…provides a rich array of constructs that describe many types of change” (Guastello & Liebovich, 2009, p. 5).

 

About the Workshop

In this workshop, you will learn how to integrate NDS analyses into your research. The workshop focuses on understanding NDS concepts, learning how to connect your research questions to NDS data analysis techniques, asking new questions that NDS affords, and interpreting and presenting the results of NDS analyses.

 

Schedule

State Space: Attractors & Fixed Points
Mon, July 15

The first day’s focus is on the concept of state space, which is the basis of many NDS techniques. A state space is a representation of important system variables and how those evolve over time. Related concepts include the notion of attractors and fixed points.

Approaches to Analysis
Tue, July 16

On the second day, approaches such as dynamical systems analysis and sparse identification of nonlinear dynamics will be used to investigate relationships between variables. These approaches augment analyses that are typically used with time-series data (e.g., latent growth curve modeling or growth mixture modeling). In addition, approaches to nonlinear regression and correlations will be introduced.

Deeper Understanding & Techniques
Wed, July 17

The third day will focus on a deeper understanding of the relationships within and between streams of data. The techniques used will include recurrence quantification analysis, orbital decomposition, transition (“Markov”) matrices, and methods for understanding dyad and group synchronization.

Metrics Indicating Self-organization
Thu, July 18

The fourth day will explore the idea of phases of qualitative behavior in a system, emergence, and self-organization. Metrics that can provide indications of the self-organization (e.g., power law distributions, burstiness) will be used, as will approaches for identifying phases in data, transitions between phases, and early warning signals that may indicate impending transitions.

Exploration of Theory & Presenting NDS
Fri, July 19

The last day will begin with catastrophe theory, which can be very useful in exploring stage theories and sudden transitions in a system. The workshop will end with hints and examples of how to present NDS ideas to a broader audience (such as journal reviewers).

 

Instructor

Bernard Ricca, Ph.D.
Instructor Profile

 

Expectations

This workshop assumes that you have a thorough background in graduate-level statistics, including significance testing and linear regression. Although some exposure to multilevel modeling or matrix algebra would be beneficial, neither of these are necessary. The workshop will be taught primarily in the R Statistical Environment, but no prior experience with R is required.

 

Application

Coming soon!