Variational Modelling: Energies, gradient flows, and large deviations
by Mark A. Peletier
Publisher: arXiv 2014
Number of pages: 64
The notes describe the methodology called Variational Modelling, and focus on the application to the modelling of gradient-flow systems. I describe the methodology itself in great detail, and explain why this is a rational modelling route.
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by M.W. Hirsch, Hal Smith
From the table of contents: Introduction; Strongly Order-Preserving Semiflows; Generic Convergence and Stability; Ordinary Differential Equations; Delay Differential Equations; Monotone Maps; Semilinear Parabolic Equations.
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This book is written for anyone with an interest in chaos, fractals, non-linear dynamics, or mathematics in general. It's a moderately heavy piece of work, requiring a bit of mathematical knowledge, but it is definitely not aimed at mathematicians.
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This book covers important topics like stability, hyperbolicity, bifurcation theory and chaos, topics which are essential to understand the behavior of nonlinear discrete dynamical systems. The theory is illuminated by examples and exercises.
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