In cboettig/regimeshifts: Models and Data for Ecological Regime Shifts

https://doi.org/10.1111/j.1461-0248.2007.01131.x

$$\dot A = -p_1 A + p_2 J$$ $$\dot F = p_3 (1 - p_4 F) - p_5 F A$$ $$\dot J = p_6 - J A - p_7 F J / (p_8 + F) + p_9 A$$

So:

$$\dot J = - q_1 J^2 - q_2 / (1 + J ) + q_3 J$$

library(ggplot2)

Here's the J model:

p1 <- 1
p2 <- 100
p3 <- 1
p4 <- 10
f <- function(x) - p1 * x ^ 2 -  p2 / (p3 + x)  + p4 * x 

Hello multiple stable states:

x = seq(1,10, .01)
df <- data.frame(x, f= f(x))
ggplot(df, aes(x,f)) + geom_line() + geom_hline(yintercept = 0)

Bye Bye stable state, hello collpase

p4 <- 8
df <- data.frame(x, f= f(x))
ggplot(df, aes(x,f)) + geom_line() + geom_hline(yintercept = 0)

cboettig/regimeshifts documentation built on July 19, 2019, 1:34 p.m.