# Plot G function #G_1 = \frac{r_1 N_1(t)^\omega}{1 + N_1(t)^\omega/K_1} for (omega in 1.4){ curve((r*x^omega)/(1 + (x^omega)/K) ,from=0,to=2,ylab='N(t+1)',xlab='N(t)', ylim=c(0,2),xlim=c(0,2),las=1) abline(coef = c(0,1),lty=2) mtext(text = paste('omega = ',omega,sep=''),side = 3,line = 1) while((as.numeric(Sys.time()) - as.numeric(date_time))<2){} } for (omega in seq(1,2,0.1)){ r=2 K=1 #omega=1.5 #curve((r*x^omega)/(1 + (x^omega)/K) ,from=0,to=2,ylab='N(t+1)',xlab='N(t)', # ylim=c(0,2),xlim=c(0,2),las=1) curve(-1+(r*x^omega)/(1 + (x^omega)/K)/x ,from=-3,to=2,ylab='Growth rate',xlab='N(t)', ylim=c(-1,1),xlim=c(0,2),las=1) abline(h=0) #abline(coef = c(0,1),lty=2) mtext(text = paste('omega = ',omega,sep=''),side = 3,line = 1) bv_function <- function(x,r,omega) x - r*(x^omega)/(1+(x^omega)) #allee_threshold <- uniroot(bv_function,r=r,omega=omega,interval=c(0.0001,0.9))$root #abline(v=allee_threshold,col='blue') print(100*allee_threshold/2) date_time<-Sys.time() while((as.numeric(Sys.time()) - as.numeric(date_time))<1.1){} }