#
# R
# Modelo Lotka~Volterra
# 
# 2026 março sáb,7
# by
# j
# 

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

graph_phase <- function() {

    Tipo <- 1

    i <- 0

    maxL <- 1000
    eps <- 0.025

    xmin <- 0.01
    xmax <- 5
    ymin <- 0.01
    ymax <- 5

    dx <- (xmax - xmin)/maxL
    dy <- (ymax - ymin)/maxL

    xk <- xmin

    i <- 0

    while (xk <= xmax) {

       xk <- xmin + i*dx

       yk <- ymin

       j = 0

       while ( yk <= ymax ) {

          yk <- ymin + j*dy
   
          z1 <- log(yk) - yk + log(xk) - xk + 3.5540898509
       
          z <- switch(Tipo,
                        z1,
                     )
       
          if ( abs(z) < eps ) {
    
             x <- c(x,xk)
             y <- c(y,yk)

          }

          j <- j + 1

       }
   
       i <- i + 1
        
    }

plot(x, y, pch=19, col="darkblue", cex = 0.15)
points(1,1,pch=19,col="red",cex=2)
    
}

graph_curvas <- function() {
    
    x0 <- 6
    y0 <- 2

    alpha <- 1.1
    beta <- 0.4
    gamma <- 0.4
    delta <- 0.1

    maxT <- 30

    dt <- 0.01

    xk <- x0
    yk <- y0

    tm <- 0.00

    while (tm <= maxT ) {

       drx <- alpha*xk - beta*xk*yk
       dry <- delta*xk*yk - gamma*yk
    
       xk <- xk + drx*dt
       yk <- yk + dry*dt
       tm <- tm + dt

       x <- c(x,xk)
       y <- c(y,yk)
       t <- c(t,tm)
    
     }

     plot(x, y, main = "Modelo Lotka-Volterra",pch=24, col="blue", cex = 0.25)
     points(4,2.75,pch=19,col="red",cex=2)
     text(x=4.25, y=3, labels="(4,2.75)", col="black")
     # lines(t,y, pch=24, col="darkgreen", cex = 0.25, lwd = 2, lty = 2)
     # legend("topright", legend = c("Presas", "Predadores"), 
     # col = c("blue", "darkgreen"), lty = 1:2, lwd = 2)
    
}

menu <- function(m) {

    if (m == 1) {
       graph_phase()
    }
    if (m == 2) {
       graph_curvas()
    }
}

menu(2)