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# XPPAUT PowerPoint PPT Presentation

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

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## 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

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

### 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]

• Simple model of an excitable membrane:

### Population Growth Model[3.p2-9]

• Simple model of growth:

### Introduction of Time Delay

• No closed-form solution available

• Dynamic is more interesting

### Role of IP3( )

• Base parameter values are:

### Conclusion

• XPPAUT is a powerful tool for:

• Solving ordinary and delay differential equations

• Understanding the solution through bifurcation analysis.

### 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