ABSTRACT
Mathematical conditions for monotone and order preserving flows with respect to an orthant are well known (see [3]). However, conditions for a single component of a system of ordinary differential equations to be monotone with respect to changes in a single initial value of some component in the system have not been developed. We present a graph theoretical approach to this question. An equivalent graphical condition for a flow to be order preserving with respect to an orthant will be given. Sufficient graphical conditions will be given for more general monotonicity results, including a result guaranteeing strictly positive or negative derivatives of components with respect to initial conditions.
