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Updated: Jul 26, 2026

Simulating the Mechanics of Lens Accommodation via a Manual Lens Stretcher
Published on: February 23, 2018
Stability analysis of two linear accommodation and convergence models
1Section of Neurobiology and Behavior, Division of Biological Sciences, Cornell University, Ithaca, New York 14853-2702, USA. cab39@cornell.edu
Purpose:
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.
Conclusion:
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.
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