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David A. Rosenbaum

The development of mathematical tools for describing dynamical systems has made it possible to characterize forms of behavior that could not be characterized before. This represents progress, but the enterprise runs the risk of being nothing more than curve fitting if investigators fail to identify the physical, biological, or psychological mechanisms which are common to systems that follow the same dynamical regime and which are not common to systems that do not follow the same dynamical regime.

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Joseph Hamill, Jeffrey M. Haddad and William J. McDermott

Variability is a critical aspect of a dynamical systems analysis. Because there are a number of numerical techniques that can be used in such an analysis, the calculation of variability has several issues that must be addressed. The purpose of this paper is to present a variety of quantitative methods for investigating variability from a dynamical systems perspective. The paper is divided into two major sections covering discrete and continuous methods. Each of these sections is subdivided into two sections. Within discrete methods, we discuss, first, the calculation of the discrete relative phase from a time-series history of two parameters and, second, the use of return maps. Using continuous methods, we present procedures for using angle-angle plots in the evaluation of relative phase. We then discuss the use of phase plots in the calculation of the continuous relative phase. Each of these methods presents unique problems for the researcher and the method to be used is determined by the nature of the question asked.

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Christophe Gernigon, Fabienne d’Arripe-Longueville, Didier Delignières and Grégory Ninot

Based on the dynamical systems perspective, the present study aimed to explore how states of involvement toward mastery, performance-approach, and performance-avoidance goals (Elliot & Church, 1997) flow, are interrelated, and are activated during a practice judo combat. Using a retrospective video recall method, two male national level judo competitors expressed on a computer their moment-to-moment level of involvement toward each goal. Self-confrontation interviews also based on the video were immediately conducted. Analyses of variance revealed differences in levels of each goal between periods of the combat. Windowed cross-correlation analyses showed that the patterns of relationships between the time series of the different goals considered two-by-two included either high positive, high negative, or zero correlations, depending on the moment. Qualitative data analyses supported these findings and suggested that goal involvement states emerged and fluctuated according to the ecological constraints of the situation, such as the initial contextual conditions and the course of action.

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Jill Whitall, Nadja Schott, Leah E. Robinson, Farid Bardid and Jane E. Clark

–1982); and (2) the dynamical systems period (1982–2000). We describe these two periods in some detail and highlight papers that shaped our decision to revise the characterization of this time in our history. Precursor Period (1787–1928) While not specifically self-described as motor development research, the

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Li Li

Variability has long been used as an indication of stability in the application of a dynamical systems approach to human motion (i.e., greater variability has been related to a less stable system and vise versa). This paper incorporates the probability of gait transition during walking and running at a certain speed to represent the stability of human locomotion. The mathematical representation concerning the probability of gait transition change with locomotory speed was derived for increasing walking speed and decreasing running speed. Additionally, the influence of acceleration and deceleration on the stability landscapes of walking and running was discussed based on experimental data. The influence of acceleration was also used to explain the different trends of hysteresis observed by various researchers. Walk-to-run transition speed was greater than run-to-walk transition speed, with a greater magnitude of acceleration, while the trend was reversed with a lesser acceleration magnitude. The quantitative measure of the relationship between variability and stability needs to be explored in the future.

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Patrick O. McKeon

Edited by John Parsons

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Patrick O. McKeon and Jay Hertel

Column-editor : Michael G. Dolan

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Christophe Gernigon, Walid Briki and Katie Eykens

Borrowing the dynamical systems perspective, two studies aimed to examine the potential properties of nonlinearity and history dependence of psychological momentum. Male regional-level table tennis players were asked to empathize with players in a very important contest by watching two video scenarios of a table tennis game in two separate sessions. The videos presented two inverted scenarios in which score gaps gradually increased or decreased. Competitive anxiety, self-confidence (Study 1), and goal involvement states (Study 2) were measured before each point. Cognitive and somatic anxieties decreased linearly during the increasing scenario, but increased nonlinearly in the decreasing scenario. Mastery-avoidance goals decreased nonlinearly in the increasing scenario, increased nonlinearly in the decreasing scenario, and displayed a negative hysteresis pattern. These findings offer new insights into the dynamics of psychological momentum and suggest new avenues of research.

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Ruud J. R. Den Hartigh, Paul L. C. Van Geert, Nico W. Van Yperen, Ralf F. A. Cox and Christophe Gernigon

This study on psychological momentum (PM) in sports provides the first experimental test of an interconnection between short-term PM (during a match) and long-term PM (across a series of matches). Twenty-two competitive athletes were striving to win a prize during a rowing-ergometer tournament, consisting of manipulated races. As hypothesized, athletes who had developed long-term positive PM after two successful races were less sensitive to a negative momentum scenario in the third race, compared with athletes who had developed long-term negative PM after two unsuccessful races. More specifically, the exerted efforts, perceptions of momentum, and self-efficacy were higher for participants who had developed long-term positive PM, and their perceptions of momentum and self-efficacy decreased less rapidly. These results illustrate a typical complex dynamical systems property, namely interconnected time scales, and provide deeper insights into the dynamical nature of PM.