Chaos Synchronization Between Josephson Junctions Coupled with Time Delays

Abstract

We investigate chaos synchronization between Josephson junctions coupled uni-directionally with time-delay. We demonstrate the possibility of high quality synchronization with numerical simulations of such systems. The results are of certain importance for obtaining the high power system of Josephson junctions, which is promising for practical applications.

Chaos Synchronization Between Time Delay Coupled Josephson Junctions Governed by a Central Junction

“…The same tendency also holds for the increased number of junctions. However in [21] we were able to show that high quality synchronization is still a possibility among unidirectionally coupled in a series of 9 Josephson junctions on condition that the coupling delay between the junctions are reduced significantly (hundreds of times). It is clear that there is a physical limit to such a reduction.…”

“…Figure 4a shows chaotic dynamics of the central junction ψ 1 (t). For comparison we also reproduce results of numerical simulations from [21] demonstrating 4 high quality synchronization between the end junctions coupled in series with a time delay. Figure 5 shows the error ψ 3 − ψ 1 dynamics between Josephson junctions 1 and 3 for the following set of parameters:β = 0.25, i dc = 0.3, i 0 = 0.7, Ω = 0.6, θ = 0, α s = 0.45, τ = 0.2.C 13 indicates the correlation coefficient between ψ 1 and ψ 3 .…”

“…We also underline there is no direct connection between the junctions 2, 3, 4 to be synchronized. This is a principal distinction from the connection topology considered in [21]. In [21] the Josephson junctions to be synchronized were connected unidirectionally in series ( Figure 3).…”

“…This is a principal distinction from the connection topology considered in [21]. In [21] the Josephson junctions to be synchronized were connected unidirectionally in series ( Figure 3). In Figures 1 and 3 unidirectionality of the coupling between the junctions is provided by a Ferrite Isolator-FI.…”

“…As shown in [21] the effect of the coupling delay time between junctions coupled in series on the synchronization quality is significant. As demonstrated by the numerical simulations in [21], with increasing coupling delays between the Josephson junctions correlation coefficients decay rapidly. The same tendency also holds for the increased number of junctions.…”