A general model for the dynamics of cell volume, global stability, and optimal control

DOI10.1007/S00285-010-0374-4zbMath1230.92014OpenAlexW2083134228WikidataQ51639050 ScholiaQ51639050MaRDI QIDQ659019

James D. Benson, John K. Critser, Carmen C. Chicone

Publication date: 9 February 2012

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00285-010-0374-4

zbMATH Keywords

OptimizationStabilityCellular mass transportCryobiologySufficiency theorem

Mathematics Subject Classification ID

Applications of optimal control and differential games (49N90) Cell biology (92C37) Global stability of solutions to ordinary differential equations (34D23) Optimality conditions for problems involving ordinary differential equations (49K15)

Related Items (11)

Existence and uniqueness of a periodic solution to an indefinite attractive singular equation ⋮ Existence and multiplicity of periodic solutions to differential equations with attractive singularities ⋮ Erratum to: ``Mathematical properties of pump-leak models of cell volume control and electrolyte balance ⋮ Mathematical properties of pump-leak models of cell volume control and electrolyte balance ⋮ Analytical optimal controls for the state constrained addition and removal of cryoprotective agents ⋮ A periodic model for the dynamics of cell volume ⋮ Existence and uniqueness of homoclinic solution for a Rayleigh equation with a singularity ⋮ Effect of the polydispersity of RBCs on the recovery rate of RBCs during the removal of CPAs ⋮ Multiple positive periodic solutions to Minkowski-curvature equations with a singularity of attractive type ⋮ Global stability and exact solution of an arbitrary-solute nonlinear cellular mass transport system ⋮ Periodic oscillations of a model for membrane permeability with fluctuating environmental conditions

Cites Work

• Stability properties of elementary dynamic models of membrane transport
• Optimal controls for a model with pharmacokinetics maximizing bone marrow in cancer chemo\-therapy
• Bilinear control processes. With applications to engineering, ecology, and medicine
• Geometrical and topological methods in optimal control theory
• A general model for the dynamics of the cell volume
• Ordinary Differential Equations with Applications
• Sufficient Conditions for Optimality and the Justification of the Dynamic Programming Method

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