Hello,

I'm a bit confused with the behavior of the following program:

{ from PyDSTool import * from PyDSTool.Toolbox import phaseplane as pp #==========SET UP SYSTEM========================== pars = {'a_P' : 0.9, 'gam' : .4 , 'b_P' : 0.2 , 'a_XP' : 0, 'a_PM' : 1, 'b_M' : 0.2, 'b_XM' : 0.3,'k_MP' : 0.01, 'b_X' : 0.3, 'a_PX' : 1.} icdict={'P': 0.4, 'X': 0, 'M' : 0.3} # Set up model Peq = 'a_P - gam*M*P/(k_MP + P) - b_P*P + a_XP*X' Meq = 'a_PM*P - b_M*M - b_XM*X*M' Xeq = 'a_PX*P - b_X*X' #X protein DSargs = args(name='mod1') DSargs.pars = pars DSargs.varspecs = {'P': Peq, 'X': Xeq, 'M' : Meq} DSargs.ics = icdict #initial conditions DSargs.tdomain = [0,50] # set the range of integration. #===================Domain========================================== DSargs.xdomain = { 'X': [-100, 15.],'M' : [-10,15],'P' : [-10,15]} #=================================================================== #==========================================0 ode = Generator.Vode_ODEsystem(DSargs) #==========================================0 #ode.set(algparams = {'max_pts': 500000}) fp_coord = pp.find_fixedpoints(ode, n=10, eps=1e-8) print 'Nr. of FP:', len(fp_coord) print fp_coord }

If I run it with that configuration I get the output:

Nr. of FP: 3

({'P': -0.34769564640811784, 'M': 2.3541360552183699, 'X': -1.1589854880270594}, {'P': 2.6474727845698838, 'M': 0.92976227864800787, 'X': 8.8249092818996129}, {'P': -0.0097771381617756583, 'M': -0.051398333866360696, 'X': -0.032590460539252193})

But when I make the domain actually smaller, by setting the xdomain for 'X': I only

get 2 FP:

Nr. of FP: 2

({'P': -0.34769564640809114, 'M': 2.3541360552183415, 'X': -1.1589854880269703}, {'P': 2.6474727845698833, 'M': 0.92976227864800809, 'X': 8.8249092818996111})

Note that the missed FP is also contained in the smaller domain. I came to this when I wondered what

the parameter 'n' from the 'find_fixedpoints' method is doing. In fact, when I set n<10 the 3rd FP is also

missed with the larger domain setting. I assured with mathematica that there are indeed 3FP and they

are also numerically correct with the 1st setting. So why gives a larger domain better results for FB finding,

and what controls the parameter 'n' ?

Thanks in advance and greetings,

Greg