  We study the ergodic property of a continuous-state branching process with
immigration and competition. The exponential ergodicity in a weighted total
variation distance is proved under natural assumptions. The main theorem
applies to subcritical, critical and supercritical branching mechanisms,
including all those of stable types. The proof is based on the construction of
a Markov coupling process and the choice of a nonsymmetric control function for
the distance. Those are designed to identify and to take the advantage of the
dominating factor from the branching, immigration and competition mechanisms in
different parts of the state space. The approach provides a way of finding a
lower bound of the ergodicity rate.
