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 derivatives with respect to 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. 
ODE solver
 parameters for ODE solver : Selection and detailed settings of numerical integration.
 Solver：selection of ODE solver built in MATLAB is possible.
ode45  This is based on an explicit RungeKutta formula, the DormandPrince pair. It is a onestep solver; that is, in computing y(tn), it needs only the solution at the immediately preceding time point, y(tn1). In general, ode45 is the best solver to apply as a "first try" for most problems.  ode23  This is also based on an explicit RungeKutta proposed by Bogacki and Shampine. It may be more efficient than ode45 at crude tolerances and in the presence of mild stiffness. ode23 is a onestep solver.  ode113  This is a variable order AdamsBashforthMoulton PECE solver. It may be more efficient than ode45 at stringent tolerances. ode113 is a multistep solver; that is, it normally needs the solutions at several preceding time points to compute the current solution.  ode23s};  This is based on a modified Rosenbrock formula of order 2. Because it is a onestep solver, it may be more efficient than ode15s at crude tolerances. It can solve some kinds of stiff problems for which ode15s is not effective.  ode15s  This is a variable order solver based on the numerical differentiation formulas (NDFs). These are related to but are more efficient than the backward differentiation formulas, BDFs (also known as Gear's method). Like ode113, ode15s is a multistep method solver. If you suspect that a problem is stiff or if ode45 failed or was very inefficient, try ode15s.  myself  This is a standard fixed step 4th order Runge Kutta method．It is not recommended unless under particular circumstances. 
 Initial step : The initial step size that the ODE solver uses. When using one of the preinstalled solvers, since the step size is automatically adjusted, setting an initial step size unreasonably small (enter a value of the input field too big) will result in poor computation efficiency. When selecting the myself method, its step size is simply 1/(the value of the input field).
 Relative tolerance : measures the error relative to the size of each state. The relative tolerance represents a percentage of the state's value.
 Absolute tolerance : represents the acceptable error as the value of the measured state approaches zero*1.
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)*2
 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 limit cycles and the detailed settings (for details see Ref.[1].)
 Not use this option： Out of consideration of a symmetrical property of limit cycles, i.e., normal action of BF.
 Inversion：The case of limit cycles with an inversion symmetry. Thus, the limit cycle 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 limit cycles with a permutation symmetry and a time shift. The limit cycle is an invariant under the operation by the following matrix and by the time shift:
,
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 limit cycle with an arbitrary symmetrical property. User must define the arbitrary symmetrical matrix.*3
 divided number：When the symmetry operation is carried out to a limit cycle, you must also take into account the time shift([1])．This option is given as a divided number that need to shift how long time for the period of the limit cycle.
References
 [1] Y. Katsuta and H. Kawakami，Bifurcations of periodic solutions in a nonlinear nonautonomous system with symmetry, Electronics and communications in Japan, Scripta Technica, Inc., Part 3, vol.77, no.3, pp.106116, 1994.
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.
