Title Advances in dynamics, optimization and computation : a volume dedicated to Michael Dellnitz on the occasion of his 60th birthday / Oliver Junge, Oliver Schütze, Gary Froyland, Sina Ober-Blöbaum, Kathrin Padberg-Gehle, editors

Published Cham : Springer, 2020

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Description 1 online resource (402 pages) Series Studies in Systems, Decision and Control ; v. 304 Studies in systems, decision and control ; v. 304. Contents Intro -- Preface -- Acknowledgements -- Contents -- List of Contributors -- I Dynamics -- A Continuation Approach to Computing Phase Resetting Curves -- 1 Introduction -- 2 Basic Setting and Definitions -- 3 Algorithm for Computing a Phase Resetting Curve -- 3.1 Continuation Set-Up for Rotated Representation of -- 3.2 Continuation Set-Up for the Phase Reset -- 4 Illustration of the Method with a Model Example -- 4.1 Computing the PTC -- 4.2 Loss of Invertibility -- 5 Phase Resetting in the FitzHugh-Nagumo Model -- 6 Phase Resetting in a Seven-Dimensional Sinoatrial Node Model -- 7 Conclusions 10 Evolving Towards Homeostasis -- 11 Input-Output Maps with Two Inputs -- 11.1 Catastrophe Theory Classification -- 11.2 Normal Forms and Plateaus -- 11.3 The Hyperbolic Umbilic -- 12 Gene Regulatory Networks and Housekeeping Genes -- 12.1 Gene Regulatory Networks and Homeostasis -- 12.2 Basic Structural Elements of GRNs -- 12.3 The Gene Regulatory Network for PGA2 -- References -- The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems -- 1 Introduction -- 2 Infinite Dimensional Embedding Techniques -- 3 The Core Dynamical System -- 4 Computation of Embedded Invariant Sets 4.1 A Subdivision Scheme for the Approximation of Embedded Attractors -- 4.2 A Continuation Technique for the Approximation of Embedded Unstable Manifolds -- 5 Numerical Realization of the CDS -- 5.1 Delay Differential Equations -- 5.2 Partial Differential Equations -- 6 Numerical Results -- 6.1 The Mackey-Glass Equation -- 6.2 The Kuramoto-Sivashinsky Equation -- 7 Conclusion -- References -- Set-Oriented and Finite-Element Study of Coherent Behavior in Rayleigh-Bénard Convection -- 1 Introduction -- 2 Nonautonomous Dynamics, Transfer Operators and Transport -- 3 Set-Oriented Numerical Framework 3.1 Approximation of Transfer Operator -- 3.2 Extracting Finite-Time Coherent Sets -- 3.3 Set-Oriented Computation of FTE -- 4 Finite-Element Framework -- 4.1 Disentangling Multiple Features with SEBA -- 5 Application to Rayleigh-Bénard Convection -- 5.1 2D System -- 5.2 3D System -- 6 Conclusion and Outlook -- References -- Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces -- 1 Introduction -- 2 Preliminaries -- 3 Decompositions of RKHS Operators -- 3.1 RKHS -- 3.2 RKHS Operators -- 3.3 Basis Orthonormalization and Kernel QR Decomposition Summary This book presents a collection of papers on recent advances in problems concerning dynamics, optimal control and optimization. In many chapters, computational techniques play a central role. Set-oriented techniques feature prominently throughout the book, yielding state-of-the-art algorithms for computing general invariant sets, constructing globally optimal controllers and solving multi-objective optimization problems Bibliography References-Input-Output Networks, Singularity Theory, and Homeostasis-1 Introduction-2 Thermoregulation: A Motivation for Homeostasis-3 Biochemical Input-Output Networks-3.1 Feedforward Excitation-3.2 Product Inhibition-3.3 Substrate Inhibition-3.4 Negative Feedback Loop-4 Infinitesimal Homeostasis-5 Input-Output Networks-6 Core Networks-7 Types of Infinitesimal Homeostasis-8 Low Degree Homeostasis Types-9 Singularity Theory of Input-Output Functions-9.1 Chair Points for Blocks of Degree 1 and 2-9.2 Elementary Catastrophe Theory and Homeostasis Notes 3.4 Eigendecomposition via Auxiliary Problem Includes author index Print version record Subject Dynamics. Mathematical optimization. Automatic control engineering. Computer science. Mathematical theory of computation. Applied mathematics. Maths for engineers. Technology & Engineering -- Automation. Computers -- Computer Science. Science -- Quantum Theory. Mathematics -- Applied. Technology & Engineering -- Engineering (General) Dynamics Mathematical optimization Genre/Form Electronic books Festschriften Festschriften. Form Electronic book Author Junge, Oliver Schütze, Oliver (Computer scientist) Froyland, Gary. Ober-Blöbaum, Sina Padberg-Gehle, Kathrin ISBN 9783030512644 3030512649

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