<s>
Numerical	B-Algorithm
continuation	I-Algorithm
is	O
a	O
method	O
of	O
computing	O
approximate	O
solutions	O
of	O
a	O
system	O
of	O
parameterized	O
nonlinear	O
equations	O
,	O
</s>
<s>
For	O
a	O
fixed	O
parameter	O
value	O
,	O
maps	B-Algorithm
Euclidean	O
n-space	O
into	O
itself	O
.	O
</s>
<s>
A	O
steady	O
state	O
,	O
or	O
fixed	O
point	O
,	O
of	O
a	O
parameterized	O
family	O
of	O
flows	B-Algorithm
or	O
maps	B-Algorithm
are	O
of	O
this	O
form	O
,	O
and	O
by	O
discretizing	B-Algorithm
trajectories	O
of	O
a	O
flow	O
or	O
iterating	O
a	O
map	O
,	O
periodic	O
orbits	O
and	O
heteroclinic	O
orbits	O
can	O
also	O
be	O
posed	O
as	O
a	O
solution	O
of	O
.	O
</s>
<s>
A	O
numerical	B-Algorithm
continuation	I-Algorithm
is	O
an	O
algorithm	O
which	O
takes	O
as	O
input	O
a	O
system	O
of	O
parametrized	O
nonlinear	O
equations	O
and	O
an	O
initial	O
solution	O
,	O
,	O
and	O
produces	O
a	O
set	O
of	O
points	O
on	O
the	O
solution	O
component	O
.	O
</s>
<s>
Simplicial	O
Continuation	O
,	O
or	O
Piecewise	B-Algorithm
Linear	I-Algorithm
Continuation	I-Algorithm
(	O
Allgower	O
and	O
Georg	O
)	O
is	O
based	O
on	O
three	O
basic	O
results	O
.	O
</s>
<s>
|If	O
F(x )	O
maps	B-Algorithm
IR^n	O
into	O
IR^( 	O
n-1	O
)	O
,	O
there	O
is	O
a	O
unique	O
linear	O
interpolant	O
on	O
an	O
(	O
n-1	O
)	O
-dimensional	O
simplex	O
which	O
agrees	O
with	O
the	O
function	O
values	O
at	O
the	O
vertices	O
of	O
the	O
simplex	O
.	O
</s>
<s>
Please	O
see	O
the	O
article	O
on	O
piecewise	B-Algorithm
linear	I-Algorithm
continuation	I-Algorithm
for	O
details	O
.	O
</s>
<s>
Numerical	B-Algorithm
continuation	I-Algorithm
techniques	O
have	O
found	O
a	O
great	O
degree	O
of	O
acceptance	O
in	O
the	O
study	O
of	O
chaotic	O
dynamical	O
systems	O
and	O
various	O
other	O
systems	O
which	O
belong	O
to	O
the	O
realm	O
of	O
catastrophe	O
theory	O
.	O
</s>
<s>
The	O
study	O
of	O
turbulence	O
is	O
another	O
field	O
where	O
the	O
Numerical	B-Algorithm
Continuation	I-Algorithm
techniques	O
have	O
been	O
used	O
to	O
study	O
the	O
advent	O
of	O
turbulence	O
in	O
a	O
system	O
starting	O
at	O
low	O
Reynolds	O
numbers	O
.	O
</s>
<s>
PyCont	O
:	O
A	O
Python	O
toolbox	O
for	O
numerical	B-Algorithm
continuation	I-Algorithm
and	O
bifurcation	O
.	O
</s>
<s>
This	O
problem	O
,	O
of	O
finding	O
the	O
points	O
which	O
F	O
maps	B-Algorithm
into	O
the	O
origin	O
appears	O
in	O
computer	O
graphics	O
as	O
the	O
problems	O
of	O
drawing	O
contour	O
maps	B-Algorithm
(	O
n	O
=	O
2	O
)	O
,	O
or	O
isosurface( n	O
=3	O
)	O
.	O
</s>
