1 / 21

Feed Sideward Understanding Biological Rhythms

diallo
Download Presentation

Feed Sideward Understanding Biological Rhythms

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

    1. Jim Holte University of Minnesota 1 1/15/02 Feed Sideward Understanding Biological Rhythms Jim Holte 1/15/2002

    2. Jim Holte University of Minnesota 2 1/15/02 Sessions Session 1 - Feed Sideward – Concepts and Examples, 1/15 Session 2 – Feed Sideward – Applications to Biological & Biomedical Systems, 1/31 Session 3 – Chronobiology, 2/12 Franz Hallberg and Germaine Cornalissen

    3. Jim Holte University of Minnesota 3 1/15/02 Feed Sideward Terms Simple Example Feed Back Reinvesting dividends Feed Foreward Setting money aside Feed Sideward Moving money to another account

    4. Jim Holte University of Minnesota 4 1/15/02 Introduction Feed Sideward is a coupling that shifts resources from one subsystem to another Feed Sideward #1 – feeds values of other variables into the specified variable Feed Sideward #2 – feeds changes of parameters into the specified variable. (time varying parameters) Feed Sideward #3 – feeds changes of topology by switch operations (switched systems) Tool for global analysis especially useful for biological systems

    5. Jim Holte University of Minnesota 5 1/15/02 Phase Space Laws of the physical world Ordinary differential equations Visualization of Solutions Understanding

    6. Jim Holte University of Minnesota 6 1/15/02 Phase Space The Lotka-Volterra Equations for Predator-Prey Systems H' = b*H - a*H*P P' = -d*P + c*H*P H = prey abundance, P = predator Set the parameters b = 2 growth coefficient of prey d = 1 growth coefficient of predators a = 1 rate of capture of prey per predator per unit time c = 1 rate of "conversion" of prey to predators per unit time per predator.

    7. Jim Holte University of Minnesota 7 1/15/02 Phase Space

    8. Jim Holte University of Minnesota 8 1/15/02 Coupled Oscillators Model x and y represent the "phases“ of two oscillators. Think of x and y: angular positions of two "particles" moving around the unit circle a1 = 0 x has constant angular rate a2 = 0 y has constant angular rate. Coupling when a1 or a2 non-zero

    9. Jim Holte University of Minnesota 9 1/15/02 Example Uncoupled Oscillators

    10. Jim Holte University of Minnesota 10 1/15/02 Example Coupled Oscillators

    11. Jim Holte University of Minnesota 11 1/15/02 Phase Resetting

    12. Jim Holte University of Minnesota 12 1/15/02 Example Phase Resetting

    13. Jim Holte University of Minnesota 13 1/15/02 Oscillator Entrainment

    14. Jim Holte University of Minnesota 14 1/15/02 Oscillator Entrainment Example

    15. Jim Holte University of Minnesota 15 1/15/02 Singularities

    16. Jim Holte University of Minnesota 16 1/15/02 Example - Singularities

    17. Jim Holte University of Minnesota 17 1/15/02 Feed Sideward Terms Simple Example Feed Back Reinvesting dividends Feed Foreward Setting money aside Feed Sideward Moving money to another account

    18. Jim Holte University of Minnesota 18 1/15/02 Feed Sideward Example

    19. Jim Holte University of Minnesota 19 1/15/02 Summary Feed Sideward is a coupling that shifts resources from one subsystem to another Feed Sideward #1 – feeds values of other variables into the specified variable Feed Sideward #2 – feeds changes of parameters into the specified variable. (time varying parameters) Feed Sideward #3 – feeds changes of topology by switch operations (switched systems) Tool for global analysis especially useful for biological systems

    20. Jim Holte University of Minnesota 20 1/15/02 Next Session Session 1 - Feed Sideward – Concepts and Examples, 1/15 Session 2 – Feed Sideward – Applications to Biological & Biomedical Systems, 1/31 Session 3 – Chronobiology, 2/12 Franz Hallberg and Germaine Cornelissen

    21. Jim Holte University of Minnesota 21 1/15/02 Backup

    22. Jim Holte University of Minnesota 22 1/15/02 Feed Sideward - Topics (60 min) Session 1 (14 slides) Background Concepts & Examples Phase Space (1 slide) Singularities (2 slides) * Coupled Oscillators (2 slides) Phase Resetting (2 slides) * Oscillator Entrainment (1 slide) Feed Sideward as modulation (3 slides) ** Summary (1 slide)

More Related