This paper reviews the recent advances in computational methods for nonlinear normal
modes (NNMs). Different algorithms for the computation of undamped and damped NNMs …

Extreme events, such as rogue waves, earthquakes, and stock market crashes, occur
spontaneously in many dynamical systems. Because of their usually adverse …

This book aims to provide an introduction to dynamical systems with multiple time scales. As
in any overview book, several topics are covered only quite briefly. My aim was to focus on …

Poincaré's program for the global analysis of a dynamical system starts by considering
simple solutions, such as equilibria and periodic orbits, together with their corresponding …

The computation of global invariant manifolds has seen renewed interest in recent years.
We survey different approaches for computing a global stable or unstable manifold of a …

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The reverse engineering of metabolic networks from experimental data is traditionally a
labor-intensive task requiring a priori systems knowledge. Using a proven model as a test …

The variation in the expression patterns of the gap genes in the blastoderm of the fruit fly
Drosophila melanogaster reduces over time as a result of cross regulation between these …

The problem of the derivation of hydrodynamics from the Boltzmann equation and related
dissipative systems is formulated as the problem of a slow invariant manifold in the space of …

We present an efficient numerical method for computing Fourier--Taylor expansions of (un)
stable manifolds associated with hyperbolic periodic orbits. Three features of the method are …