>>>> C:\tyson\odefiles\WinPP\UCHSC\B5_General_bifurcation.ode Parameters: |a|=-0.500000 |b|=0.500000 |c|=0.100000 dX/dt= X*(1-X)*(1+X) - Y dY/dt= (X-A)*(B-Y) - C All formulas are valid!! nvar=2 naux=0 nfix=0 nmark=0 NEQ=2 NODE=2 Used 5 constants and 76 symbols H8:10 14; NRM:14 16; SML:7 14 In commctl name=X Making browser neq=2 bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y bcol=0 names: X Y LOCBIF starts ... Initializing ... 2 1 3 1 | 2 3 0 X a | The first point | pt=0 x=-0.378698 p1=-0.5 bv=0 | Npt = 2 | pt=0 x=-0.278698 p1=-0.5 bv=0 | Double eigenvalue | pt=331 x=-0.0344064 p1=-0.5 bv=0 | Npt = 4 | pt=0 x=-0.023105 p1=-0.5 bv=0 | Maximum of parameter c is .250000E+00 | pt=401 x=-2.38311e-011 p1=-0.5 bv=3 | Zero eigenvalue : a= .894422E+00 | pt=311 x=3.24834e-006 p1=-0.5 bv=0.894422 | Neutral saddle | pt=325 x=0.274284 p1=-0.5 bv=0 | Npt = 8 | pt=0 x=0.278005 p1=-0.5 bv=0 | Npt = 9 | pt=0 x=0.503851 p1=-0.5 bv=0 | Zero eigenvalue : a= -.217483E+01 | pt=311 x=0.544006 p1=-0.5 bv=-2.17483 | Minimum (?) of parameter c is .122137E+00 | pt=412 x=0.544044 p1=-0.5 bv=3 | Npt = 12 | pt=0 x=0.664972 p1=-0.5 bv=0 | Double eigenvalue | pt=331 x=0.694011 p1=-0.5 bv=0 | Npt = 14 | pt=0 x=0.73699 p1=-0.5 bv=0 | Npt = 15 | pt=0 x=0.855778 p1=-0.5 bv=0 | Npt = 16 | pt=0 x=0.981948 p1=-0.5 bv=0 | Npt = 17 | pt=0 x=1.18562 p1=-0.5 bv=0 | Npt = 18 | pt=0 x=1.31562 p1=-0.5 bv=0 | Double eigenvalue | pt=331 x=1.32746 p1=-0.5 bv=0 | Npt = 20 | pt=0 x=1.41329 p1=-0.5 bv=0 | Npt = 21 | pt=0 x=1.493 p1=-0.5 bv=0 | Npt = 22 | pt=0 x=1.56105 p1=-0.5 bv=0 | Npt = 23 | pt=0 x=1.62083 p1=-0.5 bv=0 | Npt = 24 | pt=0 x=1.67439 p1=-0.5 bv=0 | Npt = 25 | pt=0 x=1.72306 p1=-0.5 bv=0 | Npt = 26 | pt=0 x=1.7678 p1=-0.5 bv=0 ! Computations terminated LOCBIF ends ... LOCBIF starts ... Initializing ... 2 1 3 -1 | 2 3 0 X a | The first point | pt=0 x=-0.378698 p1=-0.5 bv=0 | Npt = 2 | pt=0 x=-0.478698 p1=-0.5 bv=0 | Hopf : L1= -.525028E+00 | pt=321 x=-0.607611 p1=-0.5 bv=-0.525028 | Npt = 4 | pt=0 x=-0.703296 p1=-0.5 bv=0 | Npt = 5 | pt=0 x=-0.860545 p1=-0.5 bv=0 | Double eigenvalue | pt=331 x=-0.875955 p1=-0.5 bv=1.47913 | Minimum (?) of parameter c is -.269354E+00 | pt=412 x=-0.919044 p1=-0.5 bv=3 | Zero eigenvalue : a= .147913E+01 | pt=311 x=-0.919103 p1=-0.5 bv=1.47913 | Npt = 9 | pt=0 x=-0.952859 p1=-0.5 bv=0 | Npt = 10 | pt=0 x=-1.04774 p1=-0.5 bv=0 | Npt = 11 | pt=0 x=-1.16616 p1=-0.5 bv=0 | Npt = 12 | pt=0 x=-1.33601 p1=-0.5 bv=0 | Npt = 13 | pt=0 x=-1.52952 p1=-0.5 bv=0 | Npt = 14 | pt=0 x=-1.64053 p1=-0.5 bv=0 | Npt = 15 | pt=0 x=-1.72754 p1=-0.5 bv=0 | Npt = 16 | pt=0 x=-1.80019 p1=-0.5 bv=0 | Npt = 17 | pt=0 x=-1.86311 p1=-0.5 bv=0 | Npt = 18 | pt=0 x=-1.91895 p1=-0.5 bv=0 | Npt = 19 | pt=0 x=-1.96935 p1=-0.5 bv=0 | Npt = 20 | pt=0 x=-2.01544 p1=-0.5 bv=0 | Npt = 21 | pt=0 x=-2.05798 p1=-0.5 bv=0 ! Computations terminated LOCBIF ends ... LOCBIF starts ... Initializing ... 2 3 3 1 | 2 3 0 X a ! Incorrect number of active parameters LOCBIF ends ... LOCBIF starts ... Initializing ... 2 4 3 1 | 2 3 0 X a | The first point | pt=0 x=-0.607611 p1=-0.5 bv=0 | Npt = 2 | pt=0 x=-0.507611 p1=-0.5 bv=0 | Npt = 3 | pt=0 x=-0.317611 p1=-0.5 bv=0 | Npt = 4 | pt=0 x=-0.0759623 p1=-0.5 bv=0 | Double multiplier | pt=341 x=-0.034377 p1=-0.5 bv=0.894403 | Maximum of parameter c is .250000E+00 | pt=401 x=-9.91624e-009 p1=-0.5 bv=3 | Multiplier = 1 : a= .894403E+00 | pt=311 x=8.34816e-006 p1=-0.5 bv=0.894403 | Npt = 8 | pt=0 x=0.211189 p1=-0.5 bv=0 | Hopf | pt=321 x=0.274306 p1=-0.5 bv=0 | Npt = 10 | pt=0 x=0.419836 p1=-0.5 bv=0 | Npt = 11 | pt=0 x=0.52416 p1=-0.5 bv=0 | Multiplier = 1 : a= -.217507E+01 | pt=311 x=0.544036 p1=-0.5 bv=-2.17507 | Minimum (?) of parameter c is .122137E+00 | pt=412 x=0.544044 p1=-0.5 bv=3 | Npt = 14 | pt=0 x=0.628484 p1=-0.5 bv=0 | Double multiplier | pt=341 x=0.694086 p1=-0.5 bv=0 | Npt = 16 | pt=0 x=0.697263 p1=-0.5 bv=0 | Npt = 17 | pt=0 x=0.785435 p1=-0.5 bv=0 | Npt = 18 | pt=0 x=0.887948 p1=-0.5 bv=0 | Npt = 19 | pt=0 x=1.03859 p1=-0.5 bv=0 | Npt = 20 | pt=0 x=1.22143 p1=-0.5 bv=0 | Double multiplier | pt=341 x=1.32762 p1=-0.5 bv=0 | Npt = 22 | pt=0 x=1.34138 p1=-0.5 bv=0 | Npt = 23 | pt=0 x=1.43386 p1=-0.5 bv=0 | Npt = 24 | pt=0 x=1.51034 p1=-0.5 bv=0 | Npt = 25 | pt=0 x=1.57615 p1=-0.5 bv=0 | Npt = 26 | pt=0 x=1.63427 p1=-0.5 bv=0 | Npt = 27 | pt=0 x=1.68654 p1=-0.5 bv=0 | Npt = 28 | pt=0 x=1.7342 p1=-0.5 bv=0 | Npt = 29 | pt=0 x=1.77809 p1=-0.5 bv=0 ! Computations terminated LOCBIF ends ... LOCBIF starts ... Initializing ... 2 1 4 1 | 2 3 0 X a | The first point | pt=0 x=-9.91624e-009 p1=-0.5 bv=0.894427 | Npt = 2 | pt=0 x=0.0518954 p1=-0.4 bv=0.846612 | Npt = 3 | pt=0 x=0.233733 p1=-0.1 bv=0.672281 | Npt = 4 | pt=0 x=0.414925 p1=0.0912637 bv=0.124345 | Cusp | pt=321 x=0.432466 p1=0.0943245 bv=-0.228111 | Maximum of parameter a is .943247E-01 | pt=401 x=0.432471 p1=0.0943247 bv=1 | Minimum of parameter c is .501859E-01 | pt=402 x=0.432709 p1=0.0943243 bv=3 | Neutrality : a= -.228111E+00 | pt=311 x=0.457595 p1=0.0858503 bv=-0.228111 | Npt = 9 | pt=0 x=0.472153 p1=0.070288 bv=-0.398029 | Npt = 10 | pt=0 x=0.483021 p1=0.0508827 bv=-0.549278 | Npt = 11 | pt=0 x=0.493944 p1=0.0217748 bv=-0.728264 | Npt = 12 | pt=0 x=0.50787 p1=-0.0364409 bv=-1.00788 | Npt = 13 | pt=0 x=0.528867 p1=-0.211088 bv=-1.5877 | Npt = 14 | pt=0 x=0.550613 p1=-0.73503 bv=-2.47634 | Npt = 15 | pt=0 x=0.562656 p1=-1.73503 bv=-3.04767 | Npt = 16 | pt=0 x=0.567183 p1=-2.73503 bv=-3.23286 | Npt = 17 | pt=0 x=0.569572 p1=-3.73503 bv=-3.3143 | Npt = 18 | pt=0 x=0.57105 p1=-4.73503 bv=-3.35741 | Npt = 19 | pt=0 x=0.572056 p1=-5.73503 bv=-3.38314 | Npt = 20 | pt=0 x=0.572784 p1=-6.73503 bv=-3.39986 | Npt = 21 | pt=0 x=0.573336 p1=-7.73503 bv=-3.4114 | Npt = 22 | pt=0 x=0.573769 p1=-8.73503 bv=-3.41976 | Npt = 23 | pt=0 x=0.574118 p1=-9.73503 bv=-3.42603 ! Computations terminated LOCBIF ends ... LOCBIF starts ... Initializing ... 2 1 4 -1 | 2 3 0 X a ! Incorrect number of active parameters LOCBIF ends ... LOCBIF starts ... Initializing ... 2 1 4 -1 | 2 3 0 X a | The first point | pt=0 x=1.14293e-010 p1=-0.5 bv=0.894427 | Npt = 2 | pt=0 x=-0.0481377 p1=-0.6 bv=0.945768 | Npt = 3 | pt=0 x=-0.170631 p1=-0.9 bv=1.13371 | Neutrality : a= .126530E+01 | pt=311 x=-0.226807 p1=-1.07245 bv=1.2653 | Npt = 5 | pt=0 x=-0.365442 p1=-1.72797 bv=1.82229 | Npt = 6 | pt=0 x=-0.455069 p1=-2.72797 bv=2.45248 | Npt = 7 | pt=0 x=-0.493299 p1=-3.72797 bv=2.78429 | Npt = 8 | pt=0 x=-0.513689 p1=-4.72797 bv=2.96628 | Npt = 9 | pt=0 x=-0.526222 p1=-5.72797 bv=3.07632 | Npt = 10 | pt=0 x=-0.53467 p1=-6.72797 bv=3.14856 | Npt = 11 | pt=0 x=-0.540739 p1=-7.72797 bv=3.19908 | Npt = 12 | pt=0 x=-0.545304 p1=-8.72797 bv=3.23615 | Npt = 13 | pt=0 x=-0.548862 p1=-9.72797 bv=3.2644 ! Computations terminated LOCBIF ends ...