  Certain nonlinear systems can switch between dynamical attractors occupying
different regions of phase space, under variation of parameters or initial
states. In this work we exploit this feature to obtain reliable logic
operations. With logic output 0 or 1 mapped to dynamical attractors bounded in
distinct regions of phase space, and logic inputs encoded by a very small bias
parameter, we explicitly demonstrate that the system hops consistently in
response to an external input stream, operating effectively as a reliable logic
gate. This system offers the advantage that very low-amplitude inputs yield
highly amplified outputs. Additionally, different dynamical variables in the
system yield complementary logic operations in parallel. Further, we show that
in certain parameter regions noise aids the reliability of logic operations,
and is actually necessary for obtaining consistent outputs. This leads us to a
generalization of the concept of Logical Stochastic Resonance to attractors
more complex than fixed point states, such as periodic or chaotic attractors.
Lastly, the results are verified in electronic circuit experiments,
demonstrating the robustness of the phenomena. So we have combined the research
directions of Chaos Computing and Logical Stochastic Resonance here, and this
approach has the potential to be realized in wide-ranging systems.
