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# AUTO demo snh
#
# Bifurcations of global reinjection orbits near a saddle-node Hopf bifurcation
# compute the codimension-zero PtoE connection using homotopy
print "\n1st run - find and continue equilibrium a : x=y=0, phi=-acos(-0.5*nu2)"
# [ b would be x=y=0, phi=acos(-0.5*nu2) ]
r1 = run(e='snh',ICP=['nu1'],NDIM=3,ILP=0,ITNW=7,ITMX=10,
STOP=['HB1'],DS=0.1,DSMAX=1.0,DSMIN=1e-4,NPAR=26,
unames={1:'xgamma',2:'ygamma',3:'phigamma',4:'x',5:'y',6:'phi',
7:'x-',8:'y-',9:'phi-'},
parnames={1:'nu1',2:'nu2',3:'d',4:'codim',
5:'delta',6:'eps',7:'mu',8:'h',9:'T-',10:'T+',11:'T',
21:'sigma-'})
print "\n2nd run - switch to the periodic orbit and continue in nu1 up to 0.74"
r2 = run(r1('HB1'),ICP=['nu1','T'],IPS=2,NTST=100,
STOP=[],UZSTOP={'nu1':0.74},DSMAX=0.1)
print "\n3rd run - extend the system"
r3 = run(r2('UZ1'),ICP=['mu','h','T'],IPS=4,NDIM=6,NBC=7,NINT=1,
STOP=['BP1'],UZSTOP={},DS=-0.1,DSMAX=1)
print "\n4th run - normalize the Floquet bundle"
r4 = run(r3('BP1'),ISW=-1,DS=0.1,
STOP=[],UZSTOP={'h':1.0},DSMAX=100)
print "\n5th run - integrate away from the periodic orbit in negative time."
print "puts a starting value into sigma- (which measures the distance to W^u(b))"
print "UZ points denote intersections with W^u(b)"
r5 = run(r4('UZ1'),ISW=0,ICP=['T-','mu','T','sigma-'],NDIM=9,NBC=11,
PAR={'delta':1e-4,'codim':0},UZSTOP={'sigma-':0},DS=-1.0)
print "\n6th run - improve the connection"
r6 = run(r5('UZ1'),ICP=['T-','mu','T','delta'],
THL={'T':0,'T-':0},UZSTOP={'T-':-200})
print "\n7th run - find folds (tangencies of codimension-zero connection)"
r7 = run(r6('UZ1'),ICP=['nu1','mu','T','delta','T-'],NINT=2,ILP=1,
STOP=['LP2'],UZSTOP={},DS=-0.1,DSMAX=0.1)
print "\n8th run - continue left fold (t_b)"
t = run(r7('LP1'),ICP=['nu1','T','delta','nu2','T-','mu'],ISW=2,ISP=0,ITMX=20,
STOP=['LP1'])
r8 = merge(run(t)+run(t,DS='-'))
print "\n9th run - continue right fold (t_b)"
t = run(r7('LP2'),ICP=['nu1','T','delta','nu2','T-','mu'],ISW=2,ISP=0,
STOP=['LP1'])
r9 = merge(run(t)+run(t,DS='-'))
save(rl(r8+r9),'tb')
clean()
print "\nDone."
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