Slow-Fast Decoupling of the Disparity Convergence Eye Movements Dynamics

Abstract

In this paper we show how to separate the slow and fast dynamics of the disparity convergence of the eye movements dynamic model. The dynamic equations obtained determine the modified slow dynamics that takes into account the impact of the fast dynamics and the modified fast dynamics that takes into account the impact of the slow dynamics. The slow fast decoupling is achieved by finding analytical solutions of the transformation equations used. The transformed slow and fast subsystems have very simple forms. Having separated the slow and fast dynamics completely, neural control problems for the slow and fast eye movements dynamics can be independently studied and better understood.

Dynamics of eye movements under time varying stimuli

“…Modeling of the disparity convergence has been studied in several papers (Alvarez, Bhavsar, Semmlow, Bergen, & Pedrono, 2005;Alvarez, Semmlow, & Yuan, 1998;Alvarez, Semmlow, Yuan, & Munoz, 1999;Horng, Semmlow, Hung, & Ciuffreda, 1998;Hung, 1998;Hung, Semmlow, & Ciufferda, 1986;Jiang, Hung, & Ciuffreda, 2002;Khosroyani & Hung, 2002). In some studies (Alvarez, Jaswal, Gohel, & Biswal, 2014;Kim, Vicci, Granger-Donetti, & Alvarez, 2011;Lee, Semmlow, & Alvarez, 2012;Radisavljevic-Gajic, 2006) different problem formulations are used. Some of the papers have observed experimentally and analytically the presence of the slow and fast eye movement dynamics, (Alvarez et al, 1998;Hung et al, 1986;Jiang et al, 2002;Khosroyani & Hung, 2002;Lee et al, 2012;Radisavljevic-Gajic, 2006) .…”

“…In some studies (Alvarez, Jaswal, Gohel, & Biswal, 2014;Kim, Vicci, Granger-Donetti, & Alvarez, 2011;Lee, Semmlow, & Alvarez, 2012;Radisavljevic-Gajic, 2006) different problem formulations are used. Some of the papers have observed experimentally and analytically the presence of the slow and fast eye movement dynamics, (Alvarez et al, 1998;Hung et al, 1986;Jiang et al, 2002;Khosroyani & Hung, 2002;Lee et al, 2012;Radisavljevic-Gajic, 2006) . The analytical observation was made using the corresponding secondorder mathematical model (Alvarez et al, 1999;Horng et al, 1998).…”

Disparity Convergence Eye Movements Dynamics under Time Varying Stimuli

“…The modeling issue of the disparity convergence eye movements with separated slow and fast dynamics has been recently considered in [1] under the assumption of constant eye stimuli. In this paper we consider the slow and fast dynamic components under the assumption of time varying stimuli.…”

“…The inverse Chang transformation relates the original and the slow and fast variables as, [4] The step responses for the slow and fast dynamics (with the step magnitude equal to 1 A = , and with zero initial conditions) is considered in [1]. Here, we consider the eye stimili force to be time varying.…”

“…DECOUPLING OF THE SLOW AND FAST DYNAMICSThe system model defined in (1) can be put in the standard state space form[1] by using the change of variables…”