Related papers: The Retina as a Dynamical System
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
We report on recent developments in the dynamics and rigidity of infinite-volume homogeneous spaces, viewed through the lens of circles. By addressing four natural questions about circle packings, we highlight the interplay between…
Even during fixation the human eye is constantly in low amplitude motion, jittering over small angles in random directions at up to 100Hz. This motion results in all features of the image on the retina constantly traversing a number of…
We are offering a particular interpretation (well within the range of experimentally and theoretically accepted notions) of neural connectivity and dynamics and discuss it as the data-and-process architecture of the visual system. In this…
Cosmology is a well established research area in physics while dynamical systems are well established in mathematics. It turns out that dynamical system techniques are very well suited to study many aspects of cosmology. The aim of this…
It is argued that a diffusion may be ergodic even though the drift field has unbounded outward-directed parts. The discussion employs stochastic and numerical methods.
A brief review is given of topics relating to dynamical processes arising in nonlinear interactions between light and resonant systems (atoms or molecules) in the presence of a magnetic field.
This article presents a general description of dynamical systems using the language of enriched functors and enriched natural transformations. This framework is essential to establish the equivalence of three descriptions of dynamics -- a…
The novel proposal to invoke the split of the Ricci scalar into bulk and boundary terms in the gravitational action, opens up a new avenue of investigation into stellar dynamics. The Lagrangian contains functional forms of the bulk term…
Reasoning about objects, relations, and physics is central to human intelligence, and a key goal of artificial intelligence. Here we introduce the interaction network, a model which can reason about how objects in complex systems interact,…
We study the dynamical response of a circularly-driven rigid body, focusing on the description of intrinsic rotational behavior (reverse rotations). The model system we address is integrable but nontrivial, allowing for qualitative and…
Reaction systems are discrete dynamical systems inspired by bio-chemical processes, whose dynamical behaviour is expressed by set-theoretic operations on finite sets. Reaction systems thus provide a description of bio-chemical phenomena…
Visual perceptions often come with illusions whose physical origin are not well understood yet. The encoding of stochastic light intensity $x(t)$ into spikes with firing rate $r(t)$ at time $t$ is investigated in an experiment with retinas…
Automatic segmentation of retina vessels plays a pivotal role in clinical diagnosis of prevalent eye diseases, such as, Diabetic Retinopathy or Age-related Macular Degeneration. Due to the complex construction of blood vessels, with…
I argue that the widely adopted framework of stellar dynamics survived since 1940s, is not fitting the current knowledge on non-linear systems. Borrowed from plasma physics when several fundamental features of perturbed non-linear systems…
We characterize the local properties of an optomechanical system comprising the movable mirror of a resonator and its intracavity field, mutually coupled via radiation-pressure. Our approach shows that both the state of the mirror and the…
In neuroscience, optics and condensed matter there is ample physical evidence for multistable dynamical systems, that is, systems with a large number of attractors. The known mathematical mechanisms that lead to multiple attractors are…
Let $(X,d)$ be a compact metric space and $f:X \to X$ be a self-map. The compact dynamical system $(X,f)$ is called sensitive or sensitivity depends on initial conditions, if there is a positive constant $\delta$ such that in each non-empty…
We consider the dynamics of light rays in the trihexagonal tiling where triangles and hexagons are transparent and have equal but opposite indices of refraction. We find that almost every ray of light is dense in a region of a particular…
Networks have been studied mainly using statistical methods. Here I collect some dynamical systems tools which are useful to study both the dynamics on networks and their evolution. They include decomposition of differential dynamics,…