A discrete mathematical formalism (d-space) which is specifically designed to investigate discrete aspects of behavior is applied to the foregut of decapod crustacea. This approach differs from continuous modeling techniques in that the analysis determines a structure in which the observed behavior of the foregut is constrained. A notation for the implementation of the formalism is developed as well as a coordinate system natural to the functioning of the gastric mill. The formalism is used to organize previous observations that suggest potential courses of further experimental investigation. A detailed analysis of observed chewing modes of the gastric mill is presented, along with a discussion of the overall organization of the interrelationships between these modes. The investigation also addresses the relationship between behavioral modes of a pyloric muscle found in the shrimp Palaemon.
Two alternative hypotheses are presented to describe the relationship of the behavioral components of the gastric mill: an interlaced control scheme in which the components are freely exchanged, and a top-down control system where the chewing modes are rigidly separated into packages. Flow through regions of state space in time is found to be important in determining the relations between the discrete behavioral components. The behavior of the foregut, like that of other motor control systems, is shown to fit naturally into the d-space formalism.
Available at: http://works.bepress.com/gin_mccollum/20/