Báo Cáo Báo cáo hóa học ON MONOTONICITY OF SOLUTIONS OF DISCRETE-TIME NONNEGATIVE AND COMPARTMENTAL DYNAMICA

ON MONOTONICITY OF SOLUTIONS OF DISCRETE-TIME NONNEGATIVE AND COMPARTMENTAL DYNAMICAL SYSTEMS VIJAYSEKHAR CHELLABOINA, WASSIM M. HADDAD, JAMES M. BAILEY, AND JAYANTHY RAMAKRISHNAN

Received 27 October 2003

Nonnegative and compartmental dynamical system models are widespread in biological, physiological, and pharmacological sciences. Since the state variables of these systems are typically masses or concentrations of a physical process, it is of interest to determine necessary and sufficient conditions under which the system states possess monotonic solutions. In this paper, we present necessary and sufficient conditions for identifying discrete-time nonnegative and compartmental dynamical systems that only admit monotonic solutions.

1. Introduction Nonnegative dynamical systems are of paramount importance in analyzing dynamical systems involving dynamic states whose values are nonnegative [2, 9, 16, 17]. An important subclass of nonnegative systems is compartmental systems [1, 4, 6, 8,