Comparative analysis of one-particle mathematical models in materials science and oncology. II. Qualitative study of the equations

A system of two nonlinear first-order differential equations is analyzed that describe the dynamics of the interaction between lymphocytes and tumor cells in the body. The model utilized takes into account the effect of a magnetic field. A concept is formulated concerning the analogy between the behavior of microparticles (atoms, molecules) in a medium with traps (in materials science) and the behavior of lymphocytes in living tissue containing tumor cells (in oncology). It is established that the tools of the qualitative theory of differential equations (analogous to those applicable to oncology) can be effective in analysis of transport and transformations in materials science. __________ Translated from Poroshkovaya Metallurgiya, Nos. 1–2(447), pp. 92–98, January–February, 2006.