BF Options
Graphic display
 Graphic display : It is possible to display in real time the computed results of the bifurcation set. The single figure option controls whether a new display window is created or not at the beginning of computations.
 On : checked
 Display the results on one window for all computations.
 Off : unchecked
 Create a new window every computation. To be used for results comparison, for instance.
Newton's method
 parameters for Newton's method : Each bifurcation set are calculated to solve the simultaneous equation consisting of the equilibrium point equation or the fixed point one and the characteristic equation by using Newton's method. Each of the following items is a control parameter of this Newton method.
gmax  If the sum of all the absolute value of the variables exceeds this value, the program considers it diverged.  emax  If the sum of all the absolute value of the system variables used in the Newton method exceeds this value, the program considers it diverged.  eps  If the sum of all the absolute value of the differential values of the system variables used in the Newton method goes under this value, the program considers it converged.  feps  If the sum of all the absolute value of the system variables used in the Newton method goes under this value, the program considers it converged.  iter  Number of convergences for the Newton method. One exceeded this number, the program halts. 
Step size control
 reverse calculation switch : When starting the computation of the bifurcation set, the initial direction is considered to be along the parameter selected for the Y axis. If, for some reason, the computation stopped, this switch determines whether the following computation operates the opposite direction by using a negative step size at the initial point.
 On : When the computation stops, try to calculate the bifurcation set in the opposite direction
 Off : When the computation stops, stop the whole BF program.
 adaptive step size control : When tracing a bifurcation diagram, there are cases when adapting the parameters' variation step size to the bending of the curve can increase calculation efficiency. This switch enables or disables the step size control option.
 On : Use a variable step size
 Off : Use a fixed step size(Default setting)*1
 auto sw: While seeking for the value of the X parameter selected as the unknown variable by varying the parameter selected as Y, if the amount of the variation of the X parameter exceeds auto sw * step size, the computations are continued by switching the control for the X and the Y parameters.
Symmetrical property
 Symmetrical property：Definition of symmetrical properties of periodic points and the detailed settings
 Not use this option： Out of consideration of a symmetrical property of periodic points, i.e., normal action of BF.
 Inversion：The case of periodic points with an inversion symmetry. Thus, the periodic point have the following property:
.
 mu = 1: This case corresponds to the pitchfork bifurcation that the symmetrical property is preserved.
 mu = 1: This case corresponds to the pitchfork bifurcation that the symmetrical property is broken.
 Permutation：The case of periodic points with a permutation symmetry. The periodic point is an invariant under the operation by the following matrix:
,
where indicates the following matrix:
.
 mu=1:This case corresponds to the pitchfork bifurcation that the symmetrical property is preserved.
 mu = 1: This case corresponds to the pitchfork bifurcation that the symmetrical property is broken.
 Arbitrary：The case of the periodic point with an arbitrary symmetrical property. User must define the arbitrary symmetrical matrix.*2
 divided number：Not use for Discrete systems
Arbitrary eigenvalue
 Arbitrary eigenvalue：BF tool can be traced not only some kinds of bifurcation sets, but also parameter sets with an arbitrary eigenvalue. To select this option, users are able to configure the value of the eigenvalue of the parameter sets to be traced.
