# Christopher Stieha

## QPot

### an R package for analyzing SDEs and computing quasi-potential

#### Examples from Moore et al. 2016

Download our R Journal article on using QPot.

These examples are pdfs with code and R output and older R code. Webpages to come soon.

Example 1: Two stable equilibria pdf R code

Example 2: Limit cycle pdf R code

Example 3: Two local quasi-potentials that are difficult to combine into a global quasi-potential
R code

NOTE: Example 1 can be change to a limit cycle with

model.parms <- c(alpha = 1.5, beta = 45, delta = 10, gamma = 5, kappa = 18, mu = 4)

You will need to check boundaries!

#### Examples from Lotka-Volterra Competition

To show the usefulness of the quasi-potential, we can analyze Lotka-Volterra competition models.

Presentation on QPot pdf

These examples are R script files.

Coexistence R code

3D plot of coexistence global quasi-potential movie

Initial condition dependence with two stable equilibria R code

#### Literature

Cameron, M.K. Finding the quasipotential for nongradient SDEs.
*Physica D*, 241(18):1532–1550, 2012.
Moore, C.M., Stieha, C.R., Nolting, B.C., Cameron, M.K., and Abbott, K.C. in press. QPot: An R package for stochastic differential equation quasi-potential analysis. *The R Journal*
Nolting, B.C. and Abbott, K.C. Balls, cups, and quasi-potentials: Quantifying stability in stochastic
systems. *Ecology*, 97(4):850–864, 2016.