Pattern estimation and selection in media can give important clues to understand the
collective response to external stimulus by detecting the observable variables. Both reaction …

The fundamental mechanisms that control and regulate biological organisms exhibit a
surprising level of complexity. Oscillators are perhaps the simplest motifs that produce time …

The control of proteins by a transcription factor with periodically varying concentration
exhibits intriguing dynamical behaviour. Even though it is accepted that transcription factors …

This paper offers a review while also studying yet unexplored features of the area of chaotic
systems subjected to parameter drift of non-negligible rate, an area where the methods of …

In many applications, the two-dimensional trajectories of fluid particles are available, but
little is known about the underlying flow. Oceanic floats are a clear example. To extract …

In this introduction we list important definitions and relations that will be used throughout the
book. We will use SI units exclusively. In a departure from custom, for degenerate mixing …

The definition of climate itself cannot be given without a proper understanding of the key
ideas of long-term behavior of a system, as provided by dynamical systems theory. Hence, it …

Oscillations and noise drive many processes in biology, but how both affect the activity of the
transcription factor nuclear factor κB (NF-κB) is not understood. Here, we observe that when …

Topological chaos relies on the periodic motion of obstacles in a two-dimensional flow in
order to form nontrivial braids. This motion generates exponential stretching of material …

The tumor suppressor p53 responds to cellular stress and activates transcription programs
critical for regulating cell fate. DNA damage triggers oscillations in p53 levels with a robust …