title: Stability analysis of two linear accommodation and convergence models.
abstract: OBJECTIVE
  To perform time domain stability analysis on two widely accepted linear models of accommodation and convergence.
  
  
  METHODS
  For each model, the governing differential equations were used to compute the system matrix. The system matrices were used to calculate the respective trace and determinant from which eigen-vectors and eigenvalues were quantified. These characteristic numbers fully identified and classified the fixed points of each model and, thus, their stability.
  
  
  RESULTS
  Controller gains, time constants, and accommodation and convergence cross-links determined model stability. Accommodation and convergence cross-links have the greatest influence on stability. A model-specific transition between stabilities was identified as the product of these cross-links, AC.CA(CRITICAL). For each model, three types of fixed points are described and displayed graphically: stable node, line of nonisolated fixed points, and saddle.
  
  
  CONCLUSIONS
  We demonstrated the stability analysis of a two-dimensional linear system, working only in the time domain. The benefit of time-domain stability analysis is that it can be extended to nonlinear systems when frequency domain analysis techniques fail. Given that we live in a fundamentally nonlinear world and that the use and application of computational models is extensive, this is a valuable and important tool.
authors.affiliation: Section of Neurobiology and Behavior, Division of Biological Sciences, Cornell University, Ithaca, New York 14853-2702, USA. cab39@cornell.edu
authors.forename: C A
authors.initials: CA
authors.lastname: Blackie
authors.forename: H C
authors.initials: HC
authors.lastname: Howland
mesh_terms: D000065:Accommodation, Ocular / Q000502:physiology*; D003290:Convergence, Ocular / Q000502:physiology*; D006801:Humans; D016014:Linear Models; D013997:Time Factors