eode_stability_type {ecode}

Stability Analysis

Description

Check whether an equilibrium point is stable or not, and give the specific type (i.e. stable node, stable focus, unstable node, unstable focus, saddle, or centre). Check whether an equilibrium point is stable or not.

Usage

eode_stability_type(x, value, eps = 0.001)

Arguments

x

Object of class "eode" representing an ODE system.

value

an object of class "pp" representing a phase point in the ODE system under consideration.

eps

Precision used to check whether the input phase point is an equilibrium point. If the absolute value of any component of the phase velocity vector at a phase point is lower than eps, an error would be thrown out.

Value

a string character indicate the type of the equilbrium point.

Examples

eq1 <- function(x, y, r1 = 1, a11 = 1, a12 = 2) (r1 - a11 * x - a12 * y) * x
eq2 <- function(x, y, r2 = 1, a21 = 2, a22 = 1) (r2 - a21 * x - a22 * y) * y
x <- eode(dxdt = eq1, dydt = eq2)
eode_stability_type(x, value = pp(list(x = 0.3333, y = 0.3333)))