I have the following problem with using PyCont for studying a system. The problematic output can be seen here. Let me describe what I was trying to achieve.
For this system I know the equilibrium state that doesn't depend on the values of parameters. Also I know exact values of parameters at which Hopf bifurcation of this equilibrium happens.
First I have tried to let PyCont find Hopf bifurcation point automatically. As I see, almost all PyCont examples on Github start from this step. The Hopf bifurcation of this equilibrium happens when chi_1 = 0, so I've set initial value of chi_1 to -0.01 and ran an EP-C curve with respect to parameter chi_1. Without a line
this run doesn't even start and produces PyDSTool_ExistError: 'Problem in _compute: Failed to compute tangent vector.' message. I've supplied that initdirec vector because analytically it should be a tangent to this particular equilibrium curve. However, as you can see, after few steps all crashes down and MX point is encountered far from the desired Hopf point.
My question is: have I overlooked something? Can this run still be done, maybe by tweaking some other parameters of numerical methods? I don't know whether this independence of equilibrium from parameters can spoil numerics so much; I've tried to set a 2d problem with known equilibrium (Stuart-Landau oscillator) and Hopf point was found easily. I also don't see whether symmetries of a system (they are only discrete, by the way) can spoil something here. I'd be very glad to hear any advice on this problem and thanks very much for any help in advance!
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
Hello!
I have the following problem with using PyCont for studying a system. The problematic output can be seen here. Let me describe what I was trying to achieve.
For this system I know the equilibrium state that doesn't depend on the values of parameters. Also I know exact values of parameters at which Hopf bifurcation of this equilibrium happens.
First I have tried to let PyCont find Hopf bifurcation point automatically. As I see, almost all PyCont examples on Github start from this step. The Hopf bifurcation of this equilibrium happens when
chi_1 = 0, so I've set initial value ofchi_1to -0.01 and ran anEP-Ccurve with respect to parameterchi_1. Without a linePCargs.initdirec = {'xi_1':0.00, 'xi_2':0.0, 'xi_3':0.0, 'xi_4':0.0, 'xi_5':0.0, 'chi_1':0.01, 'chi_2':0.0, 'chi_3':0.0, 'chi_4':0.0, 'chi_5':0.0, 'psi_2':0.0, 'psi_3':0.0, 'psi_4':0.0}this run doesn't even start and produces
PyDSTool_ExistError: 'Problem in _compute: Failed to compute tangent vector.'message. I've supplied thatinitdirecvector because analytically it should be a tangent to this particular equilibrium curve. However, as you can see, after few steps all crashes down andMXpoint is encountered far from the desired Hopf point.My question is: have I overlooked something? Can this run still be done, maybe by tweaking some other parameters of numerical methods? I don't know whether this independence of equilibrium from parameters can spoil numerics so much; I've tried to set a 2d problem with known equilibrium (Stuart-Landau oscillator) and Hopf point was found easily. I also don't see whether symmetries of a system (they are only discrete, by the way) can spoil something here. I'd be very glad to hear any advice on this problem and thanks very much for any help in advance!