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# AUTO demo snh
#
# Bifurcations of global reinjection orbits near a saddle-node Hopf bifurcation
# compute the codimension-one PtoE connection via Lin's method
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=20,IPS=1,
UZR={},PAR={},STOP=['HB1'],DS=0.1,DSMAX=1.0,NPAR=26,
unames={1:'xgamma',2:'ygamma',3:'phigamma',4:'x',5:'y',6:'phi',
7:'x-',8:'y-',9:'phi-',10:'x+',11:'y+',12:'phi+'},
parnames={1:'nu1',2:'nu2',3:'d',
5:'delta',6:'eps',7:'mu',8:'h',9:'T-',10:'T+',11:'T',
21:'sigma-',22:'sigma+',23:'eta',24:'Zx',25:'Zy',26:'Zz'})
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={},DSMAX=1)
print "\n4th run - normalize the Floquet bundle"
print "also put a starting value into sigma- (which"
print "measures the distance to Sigma = { phi=pi })"
r4 = run(r3('BP1'),ISW=-1,
STOP=[],UZSTOP={'h':1.0},DSMAX=100)
print "\n5th run - integrate away from the periodic orbit, UZ points denote"
print " intersections with Sigma"
r5 = run(r4('UZ1'),ISW=0,ICP=['T-','mu','T','sigma-'],NDIM=9,NBC=11,
UZSTOP={'sigma-':0},DS=1.0)
print "\n6th run - integrate backwards from the equilibrium b : x=y=0, phi=acos(-0.5*nu2)"
print "up to Sigma + put starting data for Lin vector and Lin gap in Zx, Zy, Zz, and eta."
r6 = run(r5('UZ1'),ICP=['T+','sigma+','T-','mu','T'],NDIM=12,NBC=15,NPR=10,
UZSTOP={'sigma+':0})
print "\n7th run - close the gap (with some intermediate solutions)"
r7 = run(r6('UZ1'),ICP=['eta','nu1','delta','eps','T+','T-','mu','T'],
NBC=17,NINT=2,NPR=5,THL={'T':0,'T-':0,'T+':0},
UZSTOP={'eta':0},DS=-0.01,DSMAX=0.01)
save(r7,'closegap')
# plot this, have a look at the solution coordinates 'x-'-vs-'phi-' and 'x+'-vs-'phi+'
#plot(r7)
#wait()
print "\n8th run - keep the gap closed and continue in nu1,nu2"
start8 = load(r7('UZ1'),ICP=['nu1','mu','delta','eps','nu2','T+','T-','T'],
UZSTOP={},ILP=1,NPR=100,ISP=0,DS=0.1,DSMAX=0.1)
r8 = merge(run(start8,UZSTOP={'delta':-3e-3}) + run(start8,DS='-',STOP=['LP1']))
save(r8,'cb')
clean()
print "\nDone."
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