  We consider a discrete-time dynamical system generated by a nonlinear
operator (with four real parameters $a,b,c,d$) of ocean ecosystem. We find
conditions on the parameters under which the operator is reduced to a
$\ell$-Volterra quadratic stochastic operator mapping two-dimensional simplex
to itself. We show that if $cd(c+d)=0$ then (under some conditions on $a,b$)
this $\ell$-Volterra operator may have up to three or a countable set of fixed
points; if $cd(c+d)\ne 0$ then the operator has up to three fixed points.
Depending on the parameters the fixed points may be attracting, repelling or
saddle points. The limit behaviors of trajectories of the dynamical system are
studied. It is shown that independently on values of parameters and on initial
(starting) point all trajectories converge. Thus the operator (dynamical
system) is regular. We give some biological interpretations of our results.
