Mathematical principles of reinforcement were developed in order to (1
) account for the interaction of target responding and other behavior;
(2) provide a simple graphical representation; (3) deal with measurem
ent artifacts; and (4) permit a coherent transition from a statics to
a dynamics of behavior. Rats and pigeons were trained to make a target
response while general activity was measured with a stabilimeter. The
course of behavioral change was represented as a trajectory through a
two-dimensional behavior space. The trajectories rotated toward or aw
ay from the target dimension as the coupling between the target respon
se and the incentive was varied. Higher rates of reinforcement expande
d the trajectories; satiation and extinction contracted them. Concavit
y in some trajectories provided data for a dynamic generalization of t
he model.