Related Experiment Video
Updated: Dec 13, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Exact analytic solution for a chaotic hybrid dynamical system and its electronic realization
Ned J Corron1, Seth D Cohen2, Aubrey N Beal3
1U.S. Army Combat Capabilities Development Command Aviation & Missile Center, Redstone Arsenal, Alabama 35898, USA.
Abstract:
A novel hybrid dynamical system comprising a continuous and a discrete state is introduced and shown to exhibit chaotic dynamics. The system includes an unstable first-order filter subject to asynchronous switching of a set point according to a feedback rule. Regular samples of the continuous state yield a one-dimensional return map that is a tent function. An exact analytic solution is derived using a nonlinear transformation of a previously solved chaotic oscillator. Conjugacy to a symbolic dynamics is shown, and a practical realization of the system in an electronic circuit is demonstrated.
More Related Videos
08:35Interactive and Visualized Online Experimentation System for Engineering Education and Research
Published on: November 24, 2021
08:04Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
Related Concept Videos
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
State Space Representation
Consider an RLC circuit, a...
RLC Circuit as a Damped Oscillator
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...
Transfer Function to State Space
In an RLC...
Classification of Systems-I
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as: