Positivity

, Volume 14, Issue 2, pp 257–283 | Cite as

Monotone inequalities, dynamical systems, and paths in the positive orthant of Euclidean n-space

Article

Abstract

Given monotone operators on the positive orthant in n-dimensional Euclidean space, we explore the relation between inequalities involving those operators, and induced monotone dynamical systems. Attractivity of the origin implies stability for these systems, as well as a certain inequality, the no-joint-increase condition. Under the right perspective the converse is also true. In addition we construct an unbounded path in the set where trajectories of the dynamical system decay monotonically, i.e., we solve a positive continuous selection problem.

Keywords

Monotone operators and inequalities Positive systems Comparison functions Decay sets Omega paths Monotone selections 

Mathematics Subject Classification (2000)

Primary 47H07 Secondary 15A48 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.School of Electrical Engineering and Computer ScienceThe University of NewcastleCallaghanAustralia

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