QPot: An R Package for Stochastic Differential Equation Quasi-Potential Analysis

QPot is an R package for analyzing two-dimensional systems of stochastic differential equations. It provides users with a wide range of tools to simulate, analyze, and visualize the dynamics of these systems. One of QPot's key features is the computation of the quasi-potential, an important tool for studying stochastic systems. Quasi-potentials are particularly useful for comparing the relative stabilities of equilibria in systems with alternative stable states. This paper describes QPot's primary functions, and explains how quasi-potentials can yield insights about the dynamics of stochastic systems. Three worked examples guide users through the application of QPot's functions.

[1]  John H. Steele,et al.  A Simple Plankton Model , 1981, The American Naturalist.

[2]  M. Freidlin,et al.  Random Perturbations of Dynamical Systems , 1984 .

[3]  Hideitsu Hino,et al.  The YUIMA Project: A Computational Framework for Simulation and Inference of Stochastic Differential Equations , 2014 .

[4]  R. V. Roy,et al.  Noise-induced effects on a non-linear oscillator , 1995 .

[5]  Alexander Vladimirsky,et al.  Ordered Upwind Methods for Static Hamilton-Jacobi Equations: Theory and Algorithms , 2003, SIAM J. Numer. Anal..

[6]  Marcel Urner Simulation And Inference For Stochastic Differential Equations With R Examples , 2016 .

[7]  Leon O. Chua,et al.  Practical Numerical Algorithms for Chaotic Systems , 1989 .

[8]  Graham,et al.  Nonequilibrium potential for coexisting attractors. , 1986, Physical review. A, General physics.

[9]  J. Sethian,et al.  Ordered upwind methods for static Hamilton–Jacobi equations , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[10]  Martyn Plummer,et al.  The R Journal , 2012 .

[11]  Karline Soetaert,et al.  A Practical Guide to Ecological Modelling: Using R as a Simulation Platform , 2008 .

[12]  Karen C. Abbott,et al.  Balls, cups, and quasi‐potentials: quantifying stability in stochastic systems , 2015, Ecology.

[13]  Jeremy S. Collie,et al.  Modeling predator-prey dynamics in a fluctuating environment , 1994 .

[14]  Michael J. Grayling,et al.  phaseR: An R Package for Phase Plane Analysis of Autonomous ODE Systems , 2014, R J..

[15]  Karline Soetaert,et al.  Solving Differential Equations in R: Package deSolve , 2010 .

[16]  M. Cameron Finding the quasipotential for nongradient SDEs , 2012 .