Honeywell

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Chaos in a Linear Wave Equation
Keywords: chaos, nonlinear dynamics, wave equation
A linear system is shown to exhibit three properties usually considered indicative of chaotic dynamics. The system comprises a one-dimensional wave equation with gain that operates on a semi-infinite line. A suitable boundary condition enforces that waves remain finite. It is shown that the resulting solution set is dense with periodic orbits, contains transitive orbits, and exhibits extreme sensitivity to initial conditions. We consider the implications of such “linear chaos” for the most common and widely used definitions of chaos. Notably chaotic oscillators have been proposed as low-cost, high-speed solutions for physical random number generators to support encryption and Monte Carlo simulations. Also, the wide bandwidth and nonrepeating properties of chaotic waveforms suggest benefits for random-signal radar and spread-spectrum communications. Using chaos with linear characteristics may enable these benefits to be engineered into these and other technologies without paying the price for using highly nonlinear devices.
Ned Corron, Research Physicist
US Army AMRDEC
Redstone Arsenal, AL
USA


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