Interplay between order-parameter and system parameter dynamics: considerations on perceptual-cognitive-behavioral mode-mode transitions exhibiting positive and negative hysteresis and on response times

Abstract

A mathematical model is presented for the emergence of perceptual-cognitivebehavioral modes in psychophysical experiments in which participants are confronted with two alternatives. The model is based on the theory of self-organization and, in particular, the order parameter concept such that the emergence of a mode is conceptualized as an instability leading to the emergence of an appropriately defined order parameter. The order parameter model is merged with a second model that describes adaptation in terms of a system parameter dynamics. It is shown that the two-component model predicts hysteretic mode-mode transitions when control parameters are increased or decreased beyond critical values. The two-component model can account for both positive and negative hysteresis effects due to the interaction between order parameter and system parameter dynamics. Moreover, the model-based analysis reveals that response time curves look rather flat when response times are relatively decoupled from the mode-mode transition phenomenon. In general, response time curves exhibit a peaked close to the mode-mode transition point. In this context, the possibility is discussed that such peaked response time curves belong to the class of critical phenomena of self-organizing systems. In order to illustrate the relevance of peaked response time curves for future research and research reported in the past, results from a perceptual judgment experiment are reported, in which participants judged their ability to stand on a tilted slope for various angles of inclination. Response time curves were found that exhibited a peak around the mode-mode-transition points between "yes" and "no" responses.

Grand Unified Theories of the Brain Need Better Understanding of Behavior: The Two-Tiered Emergence of Function

“…Of further relevance to the discussion of the perception of affordances is the repeated finding of negative hysteresis. In this phenomenon the transition between modes occurs under a smaller magnitude of the control parameter in the descending sequence of the parameter than under its sequential increase, rather than the more established inverse, positive hysteresis (see Frank, 2015;Frank, Profeta, & Harrison, 2015;Kim & Frank, 2016;Lopresti-Goodman, Turvey, & Frank, 2013, and references in these papers). To model this phenomenon, Frank and colleagues used an approach that has important similarities with the one here advocated.…”

“…While those authors have not aimed to link the competition dynamics to taskrelevant information and affordances, in later work they conjectured that the competition in many cases is likely to be information-driven (Huys et al, 2014). Unbeknownst to those authors at that time, the establishment and formalization of that link has been pursued by Frank and colleagues in a number of studies (Frank, 2015;Frank et al, 2015;Kim & Frank, 2016;Lopresti-Goodman et al, 2013) in which they addressed affordance perception. In brief, Frank et al account for switches between competing mutually exclusive perceptual-cognitivebehavioral modes via a competition dynamics xi, identical to the approach pursued by Perdikis et al (2011aPerdikis et al ( , 2011b, following Ditzinger and Haken (1989) and Haken (1991).…”

A self organization perspective of non cooperative subject behavior leading to fatal shooting by law enforcement officers

“…Using a top-down modeling approach [11], it has been assumed that this approach also holds for selforganizing states whose precise description is more complicated. Human perception, action, and cognition has been addressed and mathematized using the amplitude equation approach [4,5,6,7,8,9,10,11]. For example, grasping a tool with one hand has been considered as a state associated with an amplitude.…”

“…The objective of the present theoretical study is to understand the behavior of individuals confronted by police and the decision-making process of law enforcement officers to shoot down a subject from the perspective of self-organization. To this end, mathematical modeling in terms of amplitude equations will be used as motivated by synergetics [3] (a theory of self-organization and pattern formation founded by Professor Hermann Haken) and generalized variants of synergetics, namely, quasi-attractor theory [4] and extended synergetics [5,6,7,8,9,10].…”

Dynamics of Perception of Affordances for Reaching for Self and Other

“…Conversely, positive hysteresis during the actualization of affordances is thought be the result of an increased interaction between behavioral systems and an increased stability of the respective attractors, which causes the system to transition from one stable state to another relatively slowly (and in this case, behind the parameter driving the system). Such differences in the interaction of action modes and the stability of their respective attractors may be due to different levels of 19 inhibitory feedback from perceptual and decision-making streams (Frank, Profeta, & Harrison, 2015;Kim & Frank, 2016). That is, it is possible that perceptual tasks involve feedback from a decision-making stream back down to the perceptual stream, but that this inhibitory feedback is absent in behavioral tasks.…”