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
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
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.