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# This script computes the initial circle of solutions for mu=0
# as well as the bifurcating branches which give us the
# Lagrange points. It then plots the full bifurcation diagram.
# Load 3d.c and c.3d into the AUTO CLUI
# Add a stopping condition so we only compute the loop once
# We tell AUTO to stop when parameter 16 is 0.991, parameter 1 is -0.1,
# or parameter 1 is 1.1. If parameter1 is 0.5 we just report
# a point.
# We also want to compute branches for the first 4 bifurcation
# points.
# IPS=0 tells AUTO to compute a family of equilibria.
# Compute the circle.
# This command parses returns a Python object which contains
# all of the data in the file in an easy to use format.
circle = run('3d',UZR={-16:0.991, -1:[-0.1,1.1], 1:0.5}, MXBF=-4, IPS=0)
# Use the label of the last solution of the previous calculation
# and use this solution as the starting point of the next
# calculation.
# Do not compute any bifurcating branches.
# We tell AUTO to stop when parameter 16 is 1.0, parameter 1 is -0.1,
# or parameter 1 is 1.1. If parameter1 is 0.5 we just report
# a point.
# Run the calculation
lagrangep = run(circle, MXBF=0, UZR={-16:1.0, -1:[-0.1,1.1], 1:0.5})
# Save the circle and data in b.lagrange_points, s.lagrange_points,
# and d.lagrange_points.
save(circle + lagrangep, 'lagrange_points')
# Plot the solutions
p3('lagrange_points')
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