Totally positive (TP), and
strictly totally positive (STP) differential systems are defined. These real,
first order, linear systems are characterized by the form of their coefficient
matrices, and by the decrease of the number of sign changes of their solution
vectors as functions of the independent variable. A bound is given for the
combined number of zeros of the first and last components of any particular
solution vector of STP system and a similar result is obtained for TP systems.
Examples show that no such bounds exist for the number of zeros of any other
component.
