Relative Coordination Reconsidered: A Stochastic Account

Motor Control ◽  
1998 ◽  
Vol 2 (3) ◽  
pp. 228-240 ◽  
Author(s):  
David R. Collins ◽  
Hyeongsaeng Park ◽  
Michael T. Turvey

Von Holst (1939/1973) parsed intersegmental coordination into relative and absolute to distinguish moderate and extreme forms. Kelso and DeGuzman (1992) discussed an interpretation of relative coordination in terms of the chaotic phenomenon of intermittency. The data of concern (DeGuzman & Kelso, 1991) do not, however, exclude a stochastic interpretation, which is detailed here following earlier suggestions. The key difference is modeling relative coordination by stochastic variability about weak attractors rather than by deterministic variability about remnants of attractors (”ghost attractors”). The intermittency interpretation is not robust in the presence of noise and, therefore, is not well disposed to account for uncertainty in detailing a model of behavioral data or its parameters. In contrast, the stochastic interpretation is based upon an approximation of unknown underlying processes in the form of Gaussian white noise. A stochastic method for estimating model parameters from a stationary probability distribution and a mean first passage time is illustrated using experimental and simulated data.

2012 ◽  
Vol 26 (23) ◽  
pp. 1250149 ◽  
Author(s):  
LILI JIANG ◽  
XIAOQIN LUO ◽  
DAN WU ◽  
SHIQUN ZHU

The dynamical behavior of tumor growth model driven by Lévy noise terms is investigated. For α = 2 and β = 0, the process driven by white Lévy noise approach to the standard Gaussian white noise can be viewed in the analysis of the steady-state probability distribution and the mean first-passage time. When β → 0, the index α would increase the mean first-passage time as scale σ < 0 and shorten the mean first-passage time as scale σ > 0. A nonzero β parameter induces α to decrease the mean first-passage time. Thus analyzing the initial situation of tumor is very important to obtain more therapy time.


2017 ◽  
Vol 37 (2) ◽  
pp. 191-198 ◽  
Author(s):  
Shenghong Li ◽  
Yong Huang

In this paper, the mean first-passage time of a delayed tumor cell growth system driven by colored cross-correlated noises is investigated. Based on the Novikov theorem and the method of probability density approximation, the stationary probability density function is obtained. Then applying the fastest descent method, the analytical expression of the mean first-passage time is derived. Finally, effects of different kinds of delays and noise parameters on the mean first-passage time are discussed thoroughly. The results show that the time delay included in the random force, additive noise intensity and multiplicative noise intensity play a positive role in the disappearance of tumor cells. However, the time delay included in the determined force and the correlation time lead to the increase of tumor cells.


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