Xppaut
This presentation is the property of its rightful owner.
Sponsored Links
1 / 23

XPPAUT PowerPoint PPT Presentation


  • 223 Views
  • Uploaded on
  • Presentation posted in: General

XPPAUT. Differential Equations Tool B.Ermentrout & J.Rinzel. Preliminary Remarks. Nonlinear ODEs do not usually have closed form solutions Numerical solutions are needed Qualitative analysis: phase plane analysis, bifurcation analysis,stability of steady states

Download Presentation

XPPAUT

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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Xppaut

XPPAUT

Differential Equations Tool

B.Ermentrout & J.Rinzel


Preliminary remarks

Preliminary Remarks

  • Nonlinear ODEs do not usually have closed form solutions

  • Numerical solutions are needed

  • Qualitative analysis: phase plane analysis, bifurcation analysis,stability of steady states

  • XPPAUT can do all that for us! FOR FREE!


Focus of this presentation

Focus of this presentation:

We will use XPPAUT for solving :

-FitzHugh-Nagumo model of excitable membrane

-Population growth model with time delay

-Model of intracellular Calcium regulation


Fitzhugh nagumo neuron 2 3 p161 163 4 p422 431

Fitzhugh-Nagumo Neuron[2 & 3.p161-163 & 4.p422-431]

  • Simple model of an excitable membrane:


Iapplied 0

Iapplied=0


Iapplied 0 5

Iapplied=0.5


Bifurcation diagram

Bifurcation Diagram:


Population growth model 3 p2 9

Population Growth Model[3.p2-9]

  • Simple model of growth:


Solution

Solution:


Sample curve

Sample Curve:


Introduction of time delay

Introduction of Time Delay

  • No closed-form solution available

  • Dynamic is more interesting


Oscillatory behavior in model with delay

Oscillatory Behavior in Model with Delay


Calcium regulation proc natl acad sci u s a 1990 78 1461 1465

Calcium RegulationProc.Natl.Acad.Sci. U.S.A. (1990) 78,1461-1465


Role of ip3

Role of IP3( )

  • Base parameter values are:


Ca vs time s

[Ca] vs. Time(s)


Bifurcation diagram1

Bifurcation Diagram


Calcium entry from extracellular space

Calcium Entry From Extracellular Space


Ca in er

[Ca] in ER


Bifurcation diagram2

Bifurcation Diagram


Conclusion

Conclusion

  • XPPAUT is a powerful tool for:

  • Solving ordinary and delay differential equations

  • Understanding the solution through bifurcation analysis.


References

References

  • [1] Goldbeter,A.,Dupont,G., and Berridge,M.(1990). Proc.Natl.Acad.Sci.U.S.A. 87 1461-1465.

  • [2] FitzHugh,R.(1961).Biophys J.1,445-466

  • [3] Murray J.(1989) .Mathematical Biology,1st edition,Springer-Verlag,New York.

  • [4] Fall,C, et al,(2002) Computational Cell Biology,1st edition,Springer-Verlag,New York

  • [5] Bard Ermentrout XPPAUT5.41 Differential equations tool(August,2002)

  • www.math.pitt.edu/~bard/xpp/xpp.html


  • Login