Mathematics as a Laboratory Tool

Dynamics, Delays and Noise

John Milton, Toru Ohira

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English

Springer Nature Switzerland AG
13 August 2022

Neurology & clinical neurophysiology; Maths for scientists; Life sciences: general issues; Cellular biology (cytology)

The second edition of Mathematics as a Laboratory Tool reflects the growing impact that computational science is having on the career choices made by undergraduate science and engineering students. The focus is on dynamics and the effects of time delays and stochastic perturbations (“noise”) on the regulation provided by feedback control systems. The concepts are illustrated with applications to gene regulatory networks, motor control, neuroscience and population biology. The presentation in the first edition has been extended to include discussions of neuronal excitability and bursting, multistability, microchaos, Bayesian inference, second-order delay differential equations, and the semi-discretization method for the numerical integration of delay differential equations. Every effort has been made to ensure that the material is accessible to those with a background in calculus. The text provides advanced mathematical concepts such as the Laplace and Fourier integral transforms in the form of Tools. Bayesian inference is introduced using a number of detective-type scenarios including the Monty Hall problem.

By: John Milton, Toru Ohira
Imprint: Springer Nature Switzerland AG
Country of Publication: Switzerland
Edition: 2nd ed. 2021
Dimensions: Height: 235mm, Width: 155mm,
Weight: 1.003kg
ISBN: 9783030695811
ISBN 10: 3030695816
Pages: 638
Publication Date: 13 August 2022
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Science and the Mathematics of Black Boxes.- The Mathematics of Change.- Equilibria and Steady States.- Stability.- Fixed Points: Creation and Destruction.- Transient Dynamics.- Frequency Domain I: Bode Plots and Transfer Functions.- Frequency Doman II: Fourier Analysis and Power Spectra.- Feedback and Control Systems-. Time delays.- Oscillations.- Characterizing and Manipulating Oscillations.- Beyond Limit Cycles.- Random Perturbations.- Noisy Dynamical Systems.- Random Walks.- Thermodynamic Perspectives.- Concluding Remarks.

John Milton, Professor of Biology and William R. Kenan Jr Chair n Computational Neuroscience, The Claremont Colleges; Adjunct Professor of Biotechnology, Keck Graduate Institute Toru Ohira, Professor Mathematics, Graduate School of Mathematics, Nagoya University, Japan