Related papers: The Retina as a Dynamical System
Dynamical systems across many disciplines are modeled as interacting particles or agents, with interaction rules that depend on a very small number of variables (e.g. pairwise distances, pairwise differences of phases, etc...), functions of…
Hysteresis can be defined from a dynamical systems perspective with respect to equilibrium points. Consequently, hysteresis naturally lends itself as a topic to illustrate and extend concepts in a dynamical systems course. A number of…
By folding an autonomous system of rational equations in the plane to a scalar difference equation, we show that the rational system has coexisting periodic orbits of all possible periods as well as stable aperiodic orbits for certain…
We propose the design of an original scalable image coder/decoder that is inspired from the mammalians retina. Our coder accounts for the time-dependent and also nondeterministic behavior of the actual retina. The present work brings two…
In a simplified fashion, the motion of the eyeball in its orbit consists of rotations around a fixed point. Therefore, this motion can be described in terms of the Euler's angles of rigid body dynamics. However, there is a physiological…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
This survey paper is aimed to describe a relatively new branch of symbolic dynamics which we call Arithmetic Dynamics. It deals with explicit arithmetic expansions of reals and vectors that have a "dynamical" sense. This means precisely…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
The study of biological cells in terms of mesoscopic, nonequilibrium, nonlinear, stochastic dynamics of open chemical systems provides a paradigm for other complex, self-organizing systems with ultra-fast stochastic fluctuations, short-time…
We study the phenomenon of controlling the light by light known as the optical bistability for the two-dimensional tilted Dirac system. Using the Boltzmann approach under relaxation time approximation, we find that the optical bistability…
Explainable Artificial Intelligence (AI) in the form of an interpretable and semiautomatic approach to stage grading ocular pathologies such as Diabetic retinopathy, Hypertensive retinopathy, and other retinopathies on the backdrop of major…
The model system manifesting phenomena peculiar to complex analytic maps is offered. The system is a non-autonomous ring cavity with nonlinear elements and filters,
While a great deal is known about the way the retina processes simple stimuli, our understanding of how the retina processes natural stimuli is still limited. Here we highlight some of the challenges that remain to be addressed to…
Multi-system interaction is an important and difficult problem in physics. Motivated by the experimental result of an electronic circuit element "Fractor", we introduce the concept of dynamic-order fractional dynamic system, in which the…
This article is devoted to study which conditions imply that a topological dynamical system is mean sensitive and which do not. Among other things we show that every uniquely ergodic, mixing system with positive entropy is mean sensitive.…
Retinal image of surrounding objects varies tremendously due to the changes in position, size, pose, illumination condition, background context, occlusion, noise, and nonrigid deformations. But despite these huge variations, our visual…
Analyzing the dynamics of open quantum systems has a long history in mathematics and physics. Depending on the system at hand, basic physical phenomena that one would like to explain are, for example, convergence to equilibrium, the…
The brain is an intricately structured organ responsible for the rich emergent dynamics that support the complex cognitive functions we enjoy as humans. With around $10^{11}$ neurons and $10^{15}$ synapses, understanding how the human brain…
Structure and dynamics of real nanosystems emerge from the unreduced solution of the underlying interaction problem. It has the property of dynamic multivaluedness giving genuine dynamic randomness and complexity (physics/9806002,…
In dynamical systems composed of interacting parts, conditional exponents, conditional exponent entropies and cylindrical entropies are shown to be well defined ergodic invariants which characterize the dynamical selforganization and…