Advances in dynamics, optimization and computation : a volume dedicated to Michael Dellnitz on the occasion of his 60th birthday /: a volume dedicated to Michael Dellnitz on the occasion of his 60th birthday. (2020)

• Record Type: Book
• Further Information: Note: Oliver Junge, Oliver Schütze, Gary Froyland, Sina Ober-Blöbaum, Kathrin Padberg-Gehle, editors.
• Other Names: Junge, Oliver; (Computer scientist), Schütze, Oliver; Froyland, Gary; Ober-Blöbaum, Sina; Padberg-Gehle, Kathrin
• 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
• Publisher Details: Cham : Springer
• Publication Date: 2020
• Extent: 1 online resource (402 pages)
• Subjects: 515/.39; Dynamics; Mathematical optimization; Electronic books
• Languages: English
• ISBNs: 9783030512644; 3030512649
• Related ISBNs: 9783030512637
• Notes: Note: 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; Note: Print version record.
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