We consider a cluster system in which each cluster is characterized
by two parameters: an \order" i; following Horton-Strahler's rules, and a
\mass" j following the usual additive rule. Denoting by ci;j (t) the concen-
tration of clusters of order i and mass j at time t; we derive a coagulation-
like ordinary di erential system for the time dynamics of these clusters.
Results about existence and the behaviour of solutions as t ! 1 are ob-
tained, in particular we prove that ci;j (t) ! 0 and Ni(c(t)) ! 0 as t ! 1;
where the functional Ni( ) measures the total amount of clusters of a given
xed order i: Exact and approximate equations for the time evolution of
these functionals are derived. We also present numerical results that sug-
gest the existence of self-similar solutions to these approximate equations
and discuss its possible relevance for an interpretation of Horton's law of
river number
