TY - JOUR
T1 - Qualitative models and experimental investigation of chaotic NOR gates and set/reset flip-flops
AU - Rahman, Aminur
AU - Jordan, Ian
AU - Blackmore, Denis
N1 - Funding Information:
Data accessibility. The data for the experiments are provided in text. All of the codes used in the simulations are available as the electronic supplementary material. Authors’ contributions. A.R. and D.B. conceived the ideas and developed the theory. A.R. designed the experiments. I.J. conducted the experiments. All authors contributed in writing/editing and gave their final approval for publication. Competing interests. We have no competing interests. Funding. I.J. was funded by the NJIT URI phase-1 and phase-2 undergraduate student seed grants with A.R. as graduate student mentor and D.B. as faculty mentor. Acknowledgements. The authors give their sincere thanks to the NJIT URI phase-1 and phase-2 undergraduate student seed grant for funding this project. D.B. and A.R. appreciate the support of DMS at NJIT, and I.J. appreciates the support of ECE at NJIT. The authors also thank Parth Sojitra for spotting a bug in an early version of the circuit. Finally, the authors express their gratitude to the reviewers for the detailed suggestions leading to the improvement of this article.
Publisher Copyright:
© 2018 The Author(s) Published by the Royal Society. All rights reserved.
PY - 2018
Y1 - 2018
N2 - It has been observed through experiments and SPICE simulations that logical circuits based upon Chua’s circuit exhibit complex dynamical behaviour. This behaviour can be used to design analogues of more complex logic families and some properties can be exploited for electronics applications. Some of these circuits have been modelled as systems of ordinary differential equations. However, as the number of components in newer circuits increases so does the complexity. This renders continuous dynamical systems models impractical and necessitates new modelling techniques. In recent years, some discrete dynamical models have been developed using various simplifying assumptions. To create a robust modelling framework for chaotic logical circuits, we developed both deterministic and stochastic discrete dynamical models, which exploit the natural recurrence behaviour, for two chaotic NOR gates and a chaotic set/reset flip-flop. This work presents a complete applied mathematical investigation of logical circuits. Experiments on our own designs of the above circuits are modelled and the models are rigorously analysed and simulated showing surprisingly close qualitative agreement with the experiments. Furthermore, the models are designed to accommodate dynamics of similarly designed circuits. This will allow researchers to develop ever more complex chaotic logical circuits with a simple modelling framework.
AB - It has been observed through experiments and SPICE simulations that logical circuits based upon Chua’s circuit exhibit complex dynamical behaviour. This behaviour can be used to design analogues of more complex logic families and some properties can be exploited for electronics applications. Some of these circuits have been modelled as systems of ordinary differential equations. However, as the number of components in newer circuits increases so does the complexity. This renders continuous dynamical systems models impractical and necessitates new modelling techniques. In recent years, some discrete dynamical models have been developed using various simplifying assumptions. To create a robust modelling framework for chaotic logical circuits, we developed both deterministic and stochastic discrete dynamical models, which exploit the natural recurrence behaviour, for two chaotic NOR gates and a chaotic set/reset flip-flop. This work presents a complete applied mathematical investigation of logical circuits. Experiments on our own designs of the above circuits are modelled and the models are rigorously analysed and simulated showing surprisingly close qualitative agreement with the experiments. Furthermore, the models are designed to accommodate dynamics of similarly designed circuits. This will allow researchers to develop ever more complex chaotic logical circuits with a simple modelling framework.
KW - Chaos
KW - NOR gate
KW - Set/reset flip-flop circuit
KW - Stochastic dynamical system
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U2 - 10.1098/rspa.2017.0111
DO - 10.1098/rspa.2017.0111
M3 - Article
AN - SCOPUS:85048046168
SN - 1364-5021
VL - 474
JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
IS - 2209
M1 - 20170111
ER -