  In a standard bifurcation of a dynamical system, the stationary points (or
more generally attractors) change qualitatively when varying a control
parameter. Here we describe a novel unusual effect, when the change of a
parameter, e.g. a growth rate, does not influence the stationary states, but
nevertheless leads to a qualitative change of dynamics. For instance, such a
dynamic transition can be between the convergence to a stationary state and a
strong increase without stationary states, or between the convergence to one
stationary state and that to a different state. This effect is illustrated for
a dynamical system describing two symbiotic populations, one of which exhibits
a growth rate larger than the other one. We show that, although the stationary
states of the dynamical system do not depend on the growth rates, the latter
influence the boundary of the basins of attraction. This change of the basins
of attraction explains this unusual effect of the quantitative change of
dynamics by growth rate variation.
