Advances in Difference Equations
Volume 2004 (2004), Issue 3, Pages 261-271

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

Copyright © 2004 VijaySekhar Chellaboina et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.