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Title: Analytically solvable chaotic oscillator based on a first-order filter

A chaotic hybrid dynamical system is introduced and its analytic solution is derived. The system is described as an unstable first order filter subject to occasional switching of a set point according to a feedback rule. The system qualitatively differs from other recently studied solvable chaotic hybrid systems in that the timing of the switching is regulated by an external clock. The chaotic analytic solution is an optimal waveform for communications in noise when a resistor-capacitor-integrate-and-dump filter is used as a receiver. As such, these results provide evidence in support of a recent conjecture that the optimal communication waveform for any stable infinite-impulse response filter is chaotic.
Authors:
; ;  [1]
  1. Charles M. Bowden Laboratory, Aviation and Missile Research, Development and Engineering Center, U.S. Army RDECOM, Redstone Arsenal, Alabama 35898 (United States)
Publication Date:
OSTI Identifier:
22482324
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 26; Journal Issue: 2; Other Information: (c) 2016 U.S. Government; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANALYTICAL SOLUTION; CAPACITORS; CHAOS THEORY; FEEDBACK; FILTERS; OSCILLATORS; RESISTORS; WAVE FORMS