Complex Dynamic Behavior In A Coupled Josephson Junction Array System With Time-delay

Josephson junction is a kind of nonlinear superconductive electronic device, which has wide prospects in application. However, there are some weaknesses for single Josephson junction, including small output power, low efficiency as coupling, etc. It has been proposed that superconductive device array systems constructed by coupling multiple Josephson junctions can overcome these weaknesses. When all Josephson junctions in a coupling array system are in the phase-locking state, the output power is maximized. Usually, the power transmission in single Josephson junction or between Josephson junctions consume some time. It is therefore significant to study the time delay effects on both single Josephson junction and coupled Josephson junction array system.In this paper, we mainly study the amplitude death phenomena and complex spatiotemporal dynamic behaviors in the coupled Josephson junction array system, including the spatiotemporal characteristics and breakup spirals in immediate coupled and time-delayed coupled time-delayed Josephson junction array system.The time-delayed Josephson junction equivalent circuit models are constructed by introducing time delay term into the known Josephson junction system, including the resistance-capacitance-shunted and resistance-capacitance-inductance-shunted Josephson junction equivalent circuit models.One-dimensional time-delayed coupled time-delayed Josephson junction array system is constructed with conjugate time-delayed variable coupling interaction. The analytical conditions of amplitude death are theoretically obtained, which are then confirmed by numerical computations and electronic circuit simulation experiments. It is helpful to effectively prevent from losing power output and significant for preparation and production of superconductive device.Basing on the known and newly constructed time-delayed Josephson junction equivalent circuit model, two-dimensional Josephson junction array systems are constructed with instantaneous and time-delayed coupling forms, respectively. Under different conditions, including boundary conditions(no-flux, periodic and fixed boundary conditions), parametric conditions(coupling strength and delay time conditions), coupling forms(spatial nearest coupling, random coupling and small world network coupling), external field conditions(steady electric field, spatially varying and temporally varying electronic fields), we found abundant and complex spatialtemporal dynamic behaviors, including spatialtemporal chaos, breakup spiral waves, dot pattern and Labyrinth pattern, etc. The breakup spiral waves are successfully controlled with the self-similar waveform control scheme through numerical computations.