Behavior of Eq. () as
changes.
,
,
. (
A)
, so that both fixed points have the same stability properties.
Curves show maximum and minimum value of
or
.
Red line shows stable equilibrium,
black, unstable equilibrium,
green circle show stable limit cycles and
blue unstable. Two points are marked by
black filled circles and the Hopf bifurcation is depicted as
HB. Apparent homoclinic is labeled
HC. (
B) Symmetric pairs of limit cycles for two different values of
τ on the curves in (
A) projected on the
plane. (
C)
so that the stability of the two equilibria is different. The maximum value of
is shown as
τ varies.
Upper curves (2) bifurcate from
and
lower curves (1) from
. Colors as in panel A.
LP denotes a limit point and
Hs denotes a Hopf bifurcation for the symmetric equilibrium
. (
D) Orbits taken from the two bifurcation curves in (
C) projected onto the
plane