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

Abstract

We study chaos synchronization between Josephson junctions governed by a central junction with a time delay and demonstrate with numerical simulations the possibility of high quality synchronization. The results are important for obtaining high power systems of Josephson junctions, which are promising for practical applications.

Modulated Feedback and Coupling Time Delays, and All-to-all Chaos Synchronisation in a Network of Networks: One of the Simplest Cases

“…Physically x is the phase lag of the electric field across the resonator (it should be noted that in the opto-electronical and acousto-optical systems x is proportional to the voltage fed to a modulator [12]);  is the relaxation coefficient for the driving x and driven y, z, u, w dynamical variables;  is the feedback loop time delay; 1  is the coupling time delay between x and y, y and z, x and u, u and w; the case will be considered as  = 1  ; m 1 ,m 2 ,m 3 ,m 4 ,m 5 are the feedback strengths for the Ikeda systems x, y, z, u, w respectively; m 6 ,m 8 ,m 7 ,m 9 are the coupling strengths between the systems x and y, y and z, x and u, u and w, respectively.…”

“…Generalised synchronisation [11] goes further in using completely different systems and associating the output of one system to a given function of the output of the other system. Coupled nonidentical oscillatory or rotatory systems can reach an intermediate regime of phase synchronisation [12][13][14], wherein locking of phases occurs, while correlation in the amplitudes remains weak. Lag synchronisation [15] is a step between phase synchronisation and complete synchronisation.…”

Characteristic distribution of finite-time Lyapunov exponents for chimera states

“…In such systems the IJJs are coupled together in a way that is essentially nonlocal; a result of the breakdown of charge neutrality [40], or a diffusion current [41,42]. IJJs could also provide a model for studying other synchronization phenomenon, such as chaos synchronization [43,44] and chimera states [45]. To this end, one of the difficulties that must first be overcome is related to the fact that, although the voltage across a stack of junctions can be measured with extreme precision, present experimental setups do not provide direct access to the voltages across individual junctions.…”

All-to-all chaos synchronization in a network of networks: One of the simplest cases

“…Synchronization in such systems is of certain importance in governing and performance improving point of view, e.g. enhancing emission power from such systems [1][2][3][4][5][6][7][8][9]. Additionally, from the fundamental point of view synchronization of coupled (chaotic) systems eliminates some degrees of freedom of the coupled system and so produces a significant reduction of complexity, thus allowing for significant simplification of computational and theoretical analysis of the system.…”

“…As synchronization in a wider sense is associated with communication, a study of existence and stability conditions for synchronization is of paramount importance in networks. Synchronization is important in chaos based communication system to decode the transmitted message [1][2][3][4][5][6][7][8][9]: At the transmitter part of the communication system a message is masked with chaos, then chaos masked message is transmitted to the receiver system. At the receiver part of the communication system due to the chaos synchronization between the transmitter and the receiver systems chaos is regenerated.…”