First Shiny webapp - Lorentz equation

server.R

library(shiny)
library(deSolve) 
library(ggplot2)

# Define server logic required to plot various variables
shinyServer(function(input, output) {
  
  solveLorenz <- function(pars, times=tout) {
    derivs <- function(t, state, pars) { # returns rate of change
      with(as.list(c(state, pars)), {
        dX <- A*X + Y*Z
        dY <- B * (Y-Z)
        dZ <- -X*Y +C*Y -Z
        return(list(c(dX, dY, dZ)))
      }
      )
    }
    state <- c(X = 34.848292, Y = 14.331027983, Z = 14.327178391) #  originally X = 1, Y = 1, Z = 1
    ## ode solves the model by integration...
    return(ode(y = state, times = times, func = derivs, parms = pars))
  }
  
  output$guessPlot <- reactivePlot(function() {
    tout<-seq(0, input$tmax, by = .01)
    guess_pars<-c(A = input$A, B = input$B, C = input$C)
#     alpha<-input$alpha
    guess <- as.data.frame(solveLorenz(guess_pars, tout))
  print(ggplot(as.data.frame(guess)) + geom_path(aes(X, Y, col=Z), alpha=input$alpha, lwd=.3))
#     plot(guess$X, guess$Y)
  })
    
})

ui.R

library(shiny)

# Define UI
shinyUI(pageWithSidebar(
  
  # Application title
  headerPanel("Test Lorentz's Equations"),
  
  # Sidebar with controls
  sidebarPanel(
    numericInput("tmax", "T:", 100),
    numericInput("alpha", "alpha:", 0.3),
    numericInput("A", "A:", -8/3),
    numericInput("B", "B:", -10),
    numericInput("C", "C:", 28)
  ),
  
  # Show the plot of the requested variable against mpg
  mainPanel(
    plotOutput("guessPlot")
  )
))