我试图获得两种竞争物种（具有空间扩散）的空间显性Lotka-Volterra竞争模型的稳定状态。这是模型（没有扩散术语）：
http://en.wikipedia.org/wiki/Competitive_Lotka%E2%80%93Volterra_equations
我让r1 = r2 = rG＆amp; alpha12 = alpha 21 = a。假设物种1的承载能力在空间x上线性变化，即K1 = x（而K2 = 0.5）。我们假设Neumann BC。空间域x为0到1.
以下是此模型在R中编码的示例：
LVcomp1D <- function (time, state, parms, N, Da, x, dx) {
with (as.list(parms), {
S1 <- state[1:N]
S2 <- state[(N+1):(2*N)]
## Dispersive fluxes; zero-gradient boundaries
FluxS1 <- -Da * diff(c(S1[1], S1, S1[N]))/dx
FluxS2 <- -Da * diff(c(S2[1], S2, S2[N]))/dx
## LV Competition
InteractS1 <- rG * S1 * (1- (S1/x)- ((a*S2)/x))
InteractS2 <- rG * S2 * (1- (S2/(K2))- ((a*S1)/(K2)))
## Rate of change = -Flux gradient + Interaction
dS1 <- -diff(FluxS1)/dx + InteractS1
dS2 <- -diff(FluxS2)/dx + InteractS2
return (list(c(dS1, dS2)))
})
}
pars <- c(rG = 1.0, a = 0.8, K2 = 0.5)
dx <- 0.001
x <- seq(0, 1, by = dx)
N <- length(x)
Da <- 0.001
state <- c(rep(0.5, N), rep(0.5, N))
print(system.time(
out <- steady.1D (y = state, func = LVcomp1D, parms = pars,
nspec = 2, N = N, x = x, dx = dx, Da = Da, pos = TRUE)
))
mf <- par(mfrow = c(2, 2))
plot(out, grid = x, xlab = "x", mfrow = NULL,
ylab = "N(x)", main = c("Species 1", "Species 2"), type = "l")
par(mfrow = mf)
问题是我无法获得模型的稳态解决方案。我不断通过x轴获得水平线。能不能帮助我，因为我不知道这段代码有什么问题。
谢谢