#
# R
#-Expoente de Lyapunov
#
# Abril 2026 Qua, 1 — Sex, 3
# by
# j
# 

x <- c()
y <- c()

lyapunov <- function() {
    
    max = 1000
    
    lmin <- 1.000
    lmax <- 4.000
    
    l <- lmin
    ldelta <- 0.001

    while (l <= lmax) {

        sum <- 0.000
        xn <- 0.5
        n <- 0
        
        while (n < max) {
            
            xn <- l*xn*(1 - xn)
            
            t <- l*(1-2*xn)
            
            if ( t != 0) {
                
                z <- log(abs(t))
                
                # cat(xn,z,'\n')
                
                sum <- sum + z
            
            }
            
            n <- n + 1
        
        }
        
        ly = (1/max)*sum

        if ( ly > 0 ) {
            # cat(l,ly,'\n')
        }

        if (ly > -5) {

            x <- c(x,l)
            y <- c(y,ly)
            
        }

        l <- l + ldelta

    }

    plot(x, y, main = 'Expoente de Lyapunov | Mapa Logistico', pch=19, col="blue", cex = 0.1)
    segments(x0 = 1,y0 = 0,x1=4,y1 = 0, col = "red")
}

lyapunov()