lv_Ndim | R Documentation |
The default simulates a system of Ndim = 4
coupled competitive Lotka-Volterra equations studied by Vano et al. (2006) using RK4 numerical integration. Vano et al. describe the dynamics of the resulting attractor as chaotic (bounded, quasi-periodic, sensitive dependence on initial conditions), also see this Wiki page.
lv_Ndim(
Nsim = 1000,
Ndim = 4,
Y0 = rep(0.1, Ndim),
r = c(1, 0.72, 1.53, 1.27),
A = matrix(c(1, 1.09, 1.52, 0, 0, 1, 0.44, 1.36, 2.33, 0, 1, 0.47, 1.21, 0.51, 0.35,
1), nrow = 4, byrow = TRUE),
K = rep(1, Ndim),
h = 0.5
)
Nsim |
How many data points to simulate (default = |
Ndim |
How many dimensions (coupled L-V equations) to use (default = |
Y0 |
A vector with |
r |
A vector with |
A |
The interaction matrix of |
K |
A vector with |
h |
The Euler parameter for RK4 integration. |
returnLongData |
Return the data in long format for easy plotting (default = |
A matrix of Ndim X Nsim
with simulated values.
Vano, J. A., Wildenberg, J. C., Anderson, M. B., Noel, J. K., & Sprott, J. C. (2006). Chaos in low-dimensional Lotka–Volterra models of competition. Nonlinearity, 19(10), 2391.
library(plot3D)
Y <- lv_Ndim()
df <- as.data.frame(apply(t(Y), 2, ts_standardise))
lines3D(df$Y1, df$Y2, df$Y3, colvar = df$Y4, clab = "Y4", xlab= "Y1", ylab = "Y2", zlab ="Y3", ticktype = "detailed")
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