On the Influence of the Coupling Strength among Chua’s Circuits on the Structure of Their Hyper-Chaotic Attractors

Abstract

The hyper-chaotic strange attractor of systems of four Chua’s circuits that are mutually coupled by three strong and three weak couplings is studied, both experimentally and via simulation. A new metric to compare strange attractors is presented. It is found that the strength of the couplings between circuits have a complex and determining influence on the probability for the presence of a trajectory within their attractors. This influence is strictly local, i.e. the probability of the presence of the trajectories is determined by the coupling strength to the directly adjacent circuits and independent of the coupling strengths among other circuits. Fluctuations in the properties of Chua’s circuits due to random fluctuations during the production of its components have a significant influence on the probability of presence of the attractor’s trajectories that could be qualitatively, but not quantitatively, modeled by our simulation. The consequences of these results for the possibility to construct “physical unclonable functions” as networks of Chua’s circuits with a hyper-chaotic dynamics are discussed.