Metastasis of malignant tumors Metastasis is the process by which cancer cells spread throughout the body and initiate tumors in various organs. This sometimes happens via the bloodstream, where cancer cells become lodged in capillaries of organs and then move across the capillary wall into the organ. Using C to denote the number of cells lodged in a capillary and I for the number that have invaded the organ, we can model this as C9 − 2C 2 C I9 − C 2 I 1 I where all constants are positive,  is the rate of movement across the capillary wall,  is the rate of dislodgment from the capillary,  is the rate at which cancer cells in the organ die, and  is their growth rate.

(a) Suppose  , . Construct the phase plane, including all nullclines, equilibria, and arrows indicating the direction of movement in the plane.

(b) Suppose  . . Construct the phase plane, including all nullclines, equilibria, and arrows indicating the direction of movement in the plane.

(c) What is the difference in the predicted dynamics between part

(a) and part (b)?

Source: Adapted from D. Kaplan et al., Understanding Nonlinear Dynamics

(New York: Springer-Verlag, 1995).