0000000000445600

AUTHOR

Elisabeth Pécou

showing 3 related works from this author

Splitting the dynamics of large biochemical interaction networks

2003

This article is inscribed in the general motivation of understanding the dynamics on biochemical networks including metabolic and genetic interactions. Our approach is continuous modeling by differential equations. We address the problem of the huge size of those systems. We present a mathematical tool for reducing the size of the model, master-slave synchronization, and fit it to the biochemical context.

Statistics and ProbabilityMaster slave synchronizationModularity (networks)Theoretical computer scienceGeneral Immunology and MicrobiologyDifferential equationSystems BiologyQuantitative Biology::Molecular NetworksApplied MathematicsSystems biologyDynamics (mechanics)Context (language use)General MedicineBiologyBioinformaticsModels BiologicalGeneral Biochemistry Genetics and Molecular BiologyCell Physiological PhenomenaGene Expression RegulationModeling and SimulationSynchronization (computer science)AnimalsGeneral Agricultural and Biological SciencesAlgorithmsJournal of Theoretical Biology
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Desychronization of one-parameter families of stable vector fields

2005

Given a one-parameter family of vector fields on , Fλ(x), , such that for each λ, Fλ has a global asymptotically stable equilibrium point xλ, we construct a vector field on of the form G(λ, x) = (g(λ, x), Fλ(x)) which exhibits chaotic behaviour. This result is an incursion in the inverse problem of master–slave synchronization.This paper discusses self-disorganization of parameter dependent stable vector fields. Motivations are found in applications to drug design: one way to lead an unfriendly organism to death is to destabilize its metabolism. In this paper we envisage the mathematical aspect of the question. We show that for a very stable system (one globally attracting equilibrium state…

Equilibrium pointPure mathematicsThermodynamic equilibriumApplied MathematicsChaoticGeneral Physics and AstronomyStatistical and Nonlinear PhysicsOf the formInverse problemDynamical systemControl theoryStability theoryVector fieldMathematical PhysicsMathematicsNonlinearity
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Topological classification of gradient-like diffeomorphisms on 3-manifolds

2004

Abstract We give a complete invariant, called global scheme , of topological conjugacy classes of gradient-like diffeomorphisms, on compact 3-manifolds. Conversely, we can realize any abstract global scheme by such a diffeomorphism.

Discrete mathematicsPure mathematicsMathematics::Dynamical SystemsTopological classificationTopological classificationGeometry and TopologyDiffeomorphismInvariant (mathematics)Topological conjugacyMathematics::Symplectic GeometryMorse–Smale diffeomorphismsMathematics3-manifoldsTopology
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