We discuss several applications of symbolic dynamics and topological analysis to problems in mathematics, physics, and engineering, based on a talk presented by Dr. 1. Introduction In September of 1997, Nick Tuullaro discussed some applications of symbolic dynamics to problems in mathematics, physics, and engineering in an IMA Industrial Problems Seminar. This article will discuss some of the a...

Covering relations are a topological tool for detecting periodic orbits, symbolic dynamics and chaotic behavior for autonomous ODE. We extend the method of the covering relations onto systems with a time dependent perturbation. As an example we apply the method to non-autonomous perturbations of the Rössler equations to show that for small perturbation they posses symbolic dynamics.

We trace the beginning of symbolic dynamics—the study of the shift dynamical system—as it arose from the use of coding to study recurrence and transitivity of geodesics. It is our assertion that neither Hadamard’s 1898 paper, nor the Morse-Hedlund papers of 1938 and 1940, which are normally cited as the first instances of symbolic dynamics, truly present the abstract point of view associated wi...

Integrate-and-Fire Mode (IFM) is a quite simple neuron model, however, it is possible to simulate circle map. With the aid of IFM, the circle map iteration of phase can be implemented, meanwhile the symbolic sequences are acquired conveniently from Integrate-and-Fire process. In this paper, the study of phase circle map model and its symbolic dynamics is made. Firstly, the partition of symbols ...

We consider recurrent neural networks which deal with symbolic formulas, terms, or, generally speaking, tree-structured data. Approaches like the recursive autoassociative memory, discrete-time recurrent networks, folding networks, tensor construction, holographic reduced representations, and recursive reduced descriptions fall into this category. They share the basic dynamics of how structured...