Monotone Systems in Biology

Abstract

Mathematical models arising in biology might sometime exhibit the remarkable feature of preserving ordering of their solutions with respect to initial data: in words, the "more" of x (the state variable) at time 0, the more of it at all subsequent times. Similar monotonicity properties are possibly exhibited also with respect to input levels. When this is the case, important features of the system's dynamics can be inferred on the basis of purely qualitative or relatively basic quantitative knowledge of the system's characteristics. We will discuss how monotonicity-related tools can be used to analyze and design biological systems with prescribed dynamical behaviors such as global stability, multistability, or periodic oscillations.