# Mackey-Glass Equation 
# Mackey & Glass (1977) Science, equation 4b
#  
#  dx(t)   beta0 theta^n x(t-tau)
#  ----- = ---------------------- - gamma x(t)
#   dt      theta^n + x(t-tau)^n
#
# Université Lyon 1, Dynamique des populations cellulaires, 2014

# parameters
p tau=6
p beta0=0.2
p gamma=0.1
p n=10
p theta=1

# nonlinear functions
f(x)=beta0*theta^n*x/(theta^n+x^n)

# equation
dx/dt=f(delay(x,tau)) - gamma*x

aux xtau=delay(x,tau)

# initial conditions
init x=0.1

# XPP settings
@ bound=1000000,total=600
@ delay=30
@ maxstor=100000
@ xp=t,yp=x,xlo=0,ylo=0,xhi=600,yhi=2.0

# AUTO bifurcation settings
@ autoxmin=0,autoxmax=22,autoymin=-0.1,autoymax=2
@ dsmax=0.5,dsmin=0.001,parmin=0.5,parmax=20

done