Strange Attractors and Short Time Series

• Speaker: Bernard Ricca, Lyda Hill Institute for Human Resilience at University of Colorado, Colorado Springs
• Abstract: The identification of strange attractors requires time series that are much longer than are typically collected in psychological investigations. This has limited the application of nonlinear dynamics in empirical studies in psychology. However, by assuming that data are sampled from a system of strange attractors, new insights into short- and mediumterm dynamics are possible using even short time series. Time series data can be used to estimate a number of attractor-like regimes that could describe the state space from which the data were collected. The sequence of transitions between these attractor-like regimes can then be used to identify trajectories of behaviors. As an example, this approach is applied to ecological momentary assessment data collected daily for seven weeks from a sample of 165 rural survivors of Hurricane Florence. This analysis resulted in 8 attractor-like regimes and 4 trajectories of behaviors. Significant differences between the regimes and some longterm outcomes of the trajectories were noted. Although a number of open questions regarding the method remain, these findings demonstrate the usefulness of the approach.

The Thirty Body Problem: Interpreting Multidimensional Dynamics at an Item Level

• Speaker: Becky Neufeld, University of Utah
• Abstract: Psychology has long used multi-item scales to capture phenomena. If we consider these items as taping into a multi-dimensional system, we have a problem where many of the items act nearly identically over time. Therefore, using multi-item scales to measure a system’s dynamics (attractors, repellors, saddles and limit cycles) can prove challenging because it is often unclear which items are contributing to a system’s underlying dynamics as well as the optimal axes that distinguish between attractive/repulsive and cyclic behavior of the system. Plenty of work has utilized the eigenvalues from the Jacobian matrix to map the primary dynamics in large multi-dimensional systems. Building on this, we draw on the parallels between the Jacobian and Factor Analysis to reinterpret the results in terms of what measurement items uniquely describe underlying dynamics. We envision this as a two-stage process paralleling exploratory factor analysis. First, we calculate the eigenvalues of a dynamic system to determine the dimensional space in which the equations function and keep only the ones that are uniquely describing the system. Secondly, we rotate these values using a varimax rotation to determine which measurement items are contributing to which dynamics. For this talk we propose using simulation examples of common psychological systems under different conditions (i.e. sleep and stress in coupled and uncoupled scenarios with varying amounts of measurement and dynamic error) to demonstrate the validity and utility of this approach for reducing multiscale measures into a manageable and interpretable number of items that optimally describe the underlying system. Joint work with Jonathan Butner, University of Utah.

Statistical Instability of Samples and Pseudo-attractors

• Speaker: Mikhail Zimin, 2554620 Ontario LTD.
• Abstract: Statistical instability of samples for living systems is described in several articles. This effect takes place for RR intervals, electromyogram, electroneurogram, and electroencephalogram. However, this phenomenon occurs not only in biological objects. For a long time, it has been observed in technical systems, where human factor is significant. So, necessity of development of new methodology for describing living systems is shown. One of its application is diagnostication of health conditions. Other actual use is taking into account human factor for adequate forecasting remaining life of equipment. Indeed, more qualified personnel can provide better maintenance and operation condition. Therefore, estima-tion of such influence and accompanying effects presents some features of interest too. In such situation the idea of a pseudo attractor may be interesting. It has a form of invariant set containing all phase paths. Wherein, different sizes of the pseudo attractor correspond to qualitatively different conditions. Besides that, form of pseudo attractors may also be helpful for diagnosing. For example, investigations were performed for electroencephalograms of persons ill with epilepsy. They are ringlike, which is qualitative differ from these pseudo-attractors of health persons having rectangular form. Number of dimensions of pseudo attractors is greater by one, than number of dimensions of confidence intervals. Correspondently it gives more useful information. Joint work with Taras Gavrilenko, Dmitry Gorbunov, Surgut State University, Maxim Zimin, 2554620 Ontario LTD., and Oksana Kulikova, the Siberian State Automobile and Highway University.