Related papers: The Retina as a Dynamical System
Model optomechanical systems with photon-vibration interactions linear, quadratic, and cubic in mechanical displacements are studied under conditions for adiabatic elimination of the photon field. The opportunity of transformation of…
An optical kink is a shock-wave-like field structure which can appear in a resonant two-level medium as a result of the nonlinear process of self-steepening. We numerically simulate this process using an adiabatically switching waveform as…
Active optics is defined as the control of the shape and the alignment of the components of an optical system at low temporal frequencies. For modern large telescopes with flexible monolithic or segmented primary mirrors and also flexible…
This paper focuses on rotational phenomena of rigid body kinematics. It discusses them in a group-theoretic approach as completely as possible, using methods and notations as intuitive as possible. With a review of current literature, this…
Limit theorems for a linear dynamical system with random interactions are established. These theorems enable us to characterize the dynamics of a large complex system in details and assess whether a large complex system is stable or…
In the paper we investigate the behavior of trajectory of rational $p$-adic dynamical system in complex $p$-adic filed $\C_p$. It is studied Siegel disks and attractors of such dynamical systems. We show that Siegel disks may either…
In this article we show that any ergodic rigid system can be topologically realized by a uniformly rigid and (topologically) weak mixing topological dynamical system.
We consider fairly general class of dynamical systems under the assumptions guaranteeing the existence of Lyapunov function around some nontrivial stationary point. Moreover, the existence of heteroclinic trajectory is proved motivated by…
Cortical activity in-vivo displays relaxational time scales much longer than the membrane time constant of the neurons or the deactivation time of ionotropic synaptic conductances. The mechanisms responsible for such slow dynamics are not…
Visually exploring the world around us is not a passive process. Instead, we actively explore the world and acquire visual information over time. Here, we present a new model for simulating human eye-movement behavior in dynamic real-world…
We consider emergence from the perspective of dynamics: states of a system evolving with time. We focus on the role of a decomposition of wholes into parts, and attempt to characterize relationships between levels without reference to…
We provide a detailed multiscale analysis of a system of particles interacting through a dynamical network of links. Starting from a microscopic model, via the mean field limit, we formally derive coupled kinetic equations for the particle…
Spatial systems with heterogeneities are ubiquitous in nature, from precipitation, temperature and soil gradients controlling vegetation growth to morphogen gradients controlling gene expression in embryos. Such systems, generally described…
Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the…
A dynamical neural network consists of a set of interconnected neurons that interact over time continuously. It can exhibit computational properties in the sense that the dynamical system's evolution and/or limit points in the associated…
We consider the collection of uniformly discrete point sets in Euclidean space equipped with the vague topology. For a point set in this collection, we characterise minimality of an associated dynamical system by almost repetitivity of the…
Optical designs for astronomy involve implementation of active optics and adaptive optics from X-ray to the infrared. Developments and results of active optics methods for telescopes, spectrographs and coronagraph planet finders are…
Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example…
Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be…
As we move through the world, the pattern of light projected on our eyes is complex and dynamic, yet we are still able to distinguish between moving and stationary objects. We propose that humans accomplish this by exploiting constraints…