Symbolic lumping of some catenary, mamillary and circular compartmental systems
E. Egri (1), J. T\'oth (2), C. Brochot (3), F. Y. Bois (3) ((1), Babe\c{s}-Bolyai University, Department of Differential Equations,, Cluj-Napoca, Romania, (2) Department of Mathematical Analysis, Budapest, University of Technology, Economics, Budapest, Hungary, (3) INERIS,
TL;DR
This paper introduces symbolic and numerical lumping methods to simplify complex compartmental systems like catenary, mamillary, and circular types, while analyzing how lumping affects their qualitative properties.
Contribution
It presents a systematic approach for symbolic lumping of key compartmental systems and explores the transformation of their qualitative properties during lumping.
Findings
Symbolic lumping effectively simplifies important compartmental models.
Numerical lumping is used for systems that are symbolically unmanageable.
Lumping transformations impact the qualitative properties of the systems.
Abstract
Some of the most important compartmental systems, such as irreversible catenary, mamillary and circular systems are symbolically simplified by the method of exact linear lumping. A few symbolically unmanageable systems are numerically lumped. Transformation of the qualitative properties under lumping are also traced.
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Taxonomy
TopicsElectrical Contact Performance and Analysis · Dielectric materials and actuators · Petri Nets in System Modeling