Chaotic attractor hopping yields logic operations.

K. Murali,Behnam Kia,Sudeshna Sinha,Vivek Kohar,William L. Ditto,Andrew Adamatzky

doi:10.1371/journal.pone.0209037

Abstract

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 0/1 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 potential to be realized in wide-ranging systems.

Highlights

Nonlinear systems yield a rich gamut of dynamical behaviors that range from fixed points and limit cycles of varying periodicities, to chaotic attractors
The input signal is very small, vis-a-vis the size of chaotic attractor, implying that a small change in the system yields a significantly different dynamical outcome
In the presence of moderate noise the system jumps from attractor to attractor in response to inputs consistently. Since these attractors are more complex than fixed points considered in earlier studies, these results offer a significant generalization of the concept of Logical Stochastic Resonance

Summary

Introduction

Nonlinear systems yield a rich gamut of dynamical behaviors that range from fixed points and limit cycles of varying periodicities, to chaotic attractors. These figures show illustrative cases of positive and negative chaotic attractors yielding Logic Output 1 and 0 respectively, under a stream of external input signals. Under a different bias parameter b, we obtain a consistent OR logic operation, again by switching between chaotic attractors confined in distinct quadrants of phase space.

Results

Conclusion