1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

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The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

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An introduction to chaotic dynamical systems

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Pattern Formation An Introduction To Methods

Ultra-light dark matter (ULDM) is a class of dark matter models (DM) where DM is composed by bosons with masses ranging from $10^{-22}\, \mathrm{eV}<m<\mathrm{eV}$. These models have been receiving a lot of attention in the past few years given their interesting property of forming a Bose-Einstein condensate (BEC) or a superfluid on galactic scales. BEC and superfluidity are one of the most striking quantum mechanical phenomena manifest on macroscopic scales, and upon condensation the particles behave as a single coherent state, described by the wavefunction of the condensate. The idea is that condensation takes place inside galaxies while outside DM behaves like a normal cold particle DM. This wave nature of DM on galactic scales that arise upon condensation can address some of the curiosities of the behaviour of DM on small scales, while maintaining the successes of LCDM on large scales. There are many models in the literature that describe a DM component that condenses in galaxies. In this review, we are going to describe those models and classify them according to the different ways they achieve condensation. For that we review the phenomena of BEC and superfluidity, and apply this knowledge to the DM in order to explain their construction and phenomenology. We describe the small scale challenges these models aim to solve and how ULDM alleviates them. These models present a rich phenomenology that is manifest in different astrophysical consequences. We review here the astrophysical and cosmological tests used to constrain those models, together with new and future observations that promise to test these models in different regimes. We finalize by showing some predictions that are a consequence of the wave nature of this component, like vortices and interference, that could represent a smoking gun in the search of these rich and interesting alternative class of DM. (Abridged)

Ultra-Light Dark Matter

Ultra-light dark matter is a class of dark matter models (DM), where DM is composed by bosons with masses ranging from $$10^{-24}\, \mathrm {eV}< m < \mathrm {eV}$$
 . These models have been receiving a lot of attention in the past few years given their interesting property of forming a Bose–Einstein condensate (BEC) or a superfluid on galactic scales. BEC and superfluidity are some of the most striking quantum mechanical phenomena that manifest on macroscopic scales, and upon condensation, the particles behave as a single coherent state, described by the wavefunction of the condensate. The idea is that condensation takes place inside galaxies while outside, on large scales, it recovers the successes of $$\varLambda $$
 CDM. This wave nature of DM on galactic scales that arise upon condensation can address some of the curiosities of the behaviour of DM on small-scales. There are many models in the literature that describe a DM component that condenses in galaxies. In this review, we are going to describe those models, and classify them into three classes, according to the different non-linear evolution and structures they form in galaxies: the fuzzy dark matter (FDM), the self-interacting fuzzy dark matter (SIFDM), and the DM superfluid. Each of these classes comprises many models, each presenting a similar phenomenology in galaxies. They also include some microscopic models like the axions and axion-like particles. To understand and describe this phenomenology in galaxies, we are going to review the phenomena of BEC and superfluidity that arise in condensed matter physics, and apply this knowledge to DM. We describe how ULDM can potentially reconcile the cold DM picture with the small-scale behaviour. These models present a rich phenomenology that is manifest in different astrophysical consequences. We review here the astrophysical and cosmological tests used to constrain those models, together with new and future observations that promise to test these models in different regimes. For the case of the FDM class, the mass where this model has an interesting phenomenology on small-scales $$ \sim 10^{-22}\, \mathrm {eV}$$
 , is strongly challenged by current observations. The parameter space for the other two classes remains weakly constrained. We finalize by showing some predictions that are a consequence of the wave nature of this component, like the creation of vortices and interference patterns, that could represent a smoking gun in the search of these rich and interesting alternative class of DM models.

/pdf/ultra-light-dark-matter-5e4ilh2w1x.pdf

Ultra-light dark matter

Poincaré maps for multiscale physics discovery and nonlinear Floquet theory

Dark disk substructure and superfluid dark matter

We investigate stationary, spatially localized patterns in lattice dynamical systems that exhibit bistability. The profiles associated with these patterns have a long plateau where the pattern resembles one of the bistable states, while the profile is close to the second bistable state outside this plateau. We show that the existence branches of such patterns generically form either an infinite stack of closed loops (isolas) or intertwined s-shaped curves (snaking). We then use bifurcation theory near the anti-continuum limit, where the coupling between edges in the lattice vanishes, to prove existence of isolas and snaking in a bistable discrete real Ginzburg–Landau equation. We also provide numerical evidence for the existence of snaking diagrams for planar localized patches on square and hexagonal lattices and outline a strategy to analyse them rigorously.

Spatially Localized Structures in Lattice Dynamical Systems

Exact minimum speed of traveling waves in a Keller–Segel model

Periodic orbits are among the simplest non-equilibrium solutions to dynamical systems, and they play a significant role in our modern understanding of the rich structures observed in many systems. For example, it is known that embedded within any chaotic attractor are infinitely many unstable periodic orbits (UPOs) and so a chaotic trajectory can be thought of as ‘jumping’ from one UPO to another in a seemingly unpredictable manner. A number of studies have sought to exploit the existence of these UPOs to control a chaotic system. These methods rely on introducing small, precise parameter manipulations each time the trajectory crosses a transverse section to the flow. Typically these methods suffer from the fact that they require a precise description of the Poincare mapping for the flow, which is a difficult task since there is no systematic way of producing such a mapping associated to a given system. Here we employ recent model discovery methods for producing accurate and parsimonious parameter-dependent Poincare mappings to stabilize UPOs in nonlinear dynamical systems. Specifically, we use the sparse identification of nonlinear dynamics (SINDy) method to frame model discovery as a sparse regression problem, which can be implemented in a computationally efficient manner. This approach provides an explicit Poincare mapping that faithfully describes the dynamics of the flow in the Poincare section and can be used to identify UPOs. For each UPO, we then determine the parameter manipulations that stabilize this orbit. The utility of these methods are demonstrated on a variety of differential equations, including the Rossler system in a chaotic parameter regime.

Jason J. Bramburger

Papers

Poincaré maps for multiscale physics discovery and nonlinear Floquet theory

Dark disk substructure and superfluid dark matter

Spatially Localized Structures in Lattice Dynamical Systems

Exact minimum speed of traveling waves in a Keller–Segel model

Data-Driven Stabilization of Periodic Orbits