Authors
Blackie, Caroline A. BOptom, MPhil; Howland, Howard C. MSc, PhD

Stability Analysis of Two Linear Accommodation and Convergence Models

publication date
Category
see more

Abstract/Introduction

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 eigenvectors and eigenvalues were quantified. These characteristic numbers fully identified and classified the fixed points of each model and, thus, their stability.


Conclusion/Results

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 ·CACRITICAL. 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.


Testimonials


  • My eight year old daughter was terrified to go to the eye doctor for fear of her eyes being dilated. The doctor was SO KID friendly! He immediately made her comfortable by engaging her in conversation. It was a geat experience.


    Joya B.

  • Dr. Garbus spent an amazing amount of time to solve my very complicated visual problems. Over the years he has continually achieved results beyond what others felt possible. He is always up to date on the latest science. He is great!


    Dolores K.

  • Family Vision Care Valencia makes it so easy. Staff is knows what they are doing and Dr. Garbus is thorough and kept me well informed during the exam.


    Kristy B.

  • I have been coming to Family Vision Center for almost 20 years. Dr. Garbus has been able to help my vision when other doctors could not. Now my kids see him as well. I highly recommend this office!


    Autumn C.

  • The Doctor is very good. I felt on this visit he seemed rushed. I had questions to ask him but he was already with another patient. I still do not know if my eyes are the same , worse, or better.


    Howard B.

Testimonials


My eight year old daughter was terrified to go to the eye doctor for fear of her eyes being dilated. The doctor was SO KID friendly! He immediately made her comfortable by engaging her in conversation. It was a geat experience.


Joya B.

Dr. Garbus spent an amazing amount of time to solve my very complicated visual problems. Over the years he has continually achieved results beyond what others felt possible. He is always up to date on the latest science. He is great!


Dolores K.

Family Vision Care Valencia makes it so easy. Staff is knows what they are doing and Dr. Garbus is thorough and kept me well informed during the exam.


Kristy B.

I have been coming to Family Vision Center for almost 20 years. Dr. Garbus has been able to help my vision when other doctors could not. Now my kids see him as well. I highly recommend this office!


Autumn C.

The Doctor is very good. I felt on this visit he seemed rushed. I had questions to ask him but he was already with another patient. I still do not know if my eyes are the same , worse, or better.


Howard B.

All the staff is friendly, helpful and knowledgeable, and has been for all the years I have been going there.


Mary Ann H.
1 2 3 13

Blog

main-2

Macular degeneration: separating fact from fiction- myths and misconceptions

Macular degeneration is the leading cause of blindness in older adults in the United States. Approximately 20 million adults in the US suffer from age-related macular degeneration (AMD). A recent study reveals that the number of AMD cases has doubled from previous estimates. In 2019, 18 million people over 40 were diagnosed with early-stage AMD, […]

Read More
frustrated-millennial-businessman-having-strong-headache-tired-from-laptop-work

Alleviating Eye Strain from Digital Devices: Tips and Exercises for Relief

As we spend more and more time in front of computer screens and cell phones, it's important to be aware of the potential effects on our eyes. Eye strain, pressure between the eyes, and headaches can be caused by prolonged device use, as well as shoulder and neck pain. In this blog, we'll provide some […]

Read More
woman-look-at-the-computer-screen-C7JER3X

Understanding Double Vision (Diplopia): Causes, Symptoms, and Treatments in Santa Clarita, CA

Each year in the United States, there are approximately 850,000 visits to eye doctors for double vision (diplopia), with 95% of these being made on an outpatient basis. The overwhelming majority of cases are treatable and not indicating a major health issue with visits from an outpatient setting. However double vision in an emergency room […]

Read More
see all blogs

Contact Us To Amplify Your EyeCare

Working Hours

Monday - Thursday
8:00 am - 5:15pm
friday-sunday
Closed
Location
28089 Smyth Drive Santa Clarita, CA 91355
Website Accessibility Policy
Safety protocols page
Amplify Eyecare Santa Clarita phone-handsetarrow-uparrow-right linkedin facebook pinterest youtube rss twitter instagram facebook-blank rss-blank linkedin-blank pinterest youtube twitter instagram