Oscillatory threshold logic.

In the 1940s, the first generation of modern computers used vacuum tube oscillators as their principle components, however, with the development of the transistor, such oscillator based computers quickly became obsolete. As the demand for faster and lower power computers continues, transistors are themselves approaching their theoretical limit and emerging technologies must eventually supersede them. With the development of optical oscillators and Josephson junction technology, we are again presented with the possibility of using oscillators as the basic components of computers, and it is possible that the next generation of computers will be composed almost entirely of oscillatory devices.

Encoding via conjugate symmetries of slow oscillations for globally coupled oscillators.

We study properties of the dynamics underlying slow cluster oscillations in two systems of five globally coupled oscillators. These slow oscillations are due to the appearance of structurally stable heteroclinic connections between cluster states in the noise-free dynamics. In the presence of low levels of noise they give rise to long periods of residence near cluster states interspersed with sudden transitions between them.