Advances in Difference Equations 
Volume 2004 (2004), Issue 3, Pages 261-271
doi:10.1155/S1687183904310095

On monotonicity of solutions of discrete-time nonnegative and compartmental dynamical systems

VijaySekhar Chellaboina,1 Wassim M. Haddad,2 James M. Bailey,3 and Jayanthy Ramakrishnan1

 1Department Mechanical and Aerospace Engineering, University of Missouri-Columbia, Columbia 65211, MO, USA
2School of Aerospace Engineering, Georgia Institute of Technology, Atlanta 30332-0150, GA, USA
3Department of Anesthesiology, Northeast Georgia Medical Center, Gainesville 30503, GA, USA
Received 27 October 2003

Abstract

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.