Bursting behaviour in coupled Josephson junctions

Magnetic Flux Sensor Based on Spiking Neurons with Josephson Junctions

Josephson junctions (JJs) are superconductor-based devices used to build highly sensitive magnetic flux sensors called superconducting quantum interference devices (SQUIDs). These sensors may vary in design, being the radio frequency (RF) SQUID, direct current (DC) SQUID, and hybrid, such as D-SQUID. In addition, recently many of JJ's applications were found in spiking models of neurons exhibiting nearly biological behavior. In this study, we propose and investigate a new circuit model of a sensory neuron based on DC SQUID as part of the circuit. The dependence of the dynamics of the designed model on the external magnetic flux is demonstrated. The design of the circuit and derivation of the corresponding differential equations that describe the dynamics of the system are given. Numerical simulation is used for experimental evaluation. The experimental results confirm the applicability and good performance of the proposed magnetic-flux-sensitive neuron concept: the considered device can encode the magnetic flux in the form of neuronal dynamics with the linear section. Furthermore, some complex behavior was discovered in the model, namely the intermittent chaotic spiking and plateau bursting. The proposed design can be efficiently applied to developing the interfaces between circuitry and spiking neural networks. However, it should be noted that the proposed neuron design shares the main limitation of all the superconductor-based technologies, i.e., the need for a cryogenic and shielding system.

Neuron-like spiking and bursting in Josephson junctions: A review

The superconducting Josephson junction shows spiking and bursting behaviors, which have similarities with neuronal spiking and bursting. This phenomenon had been observed long ago by some researchers; however, they overlooked the biological similarity of this particular dynamical feature and never attempted to interpret it from the perspective of neuronal dynamics. In recent times, the origin of such a strange property of the superconducting junction has been explained and such neuronal functional behavior has also been observed in superconducting nanowires. The history of this research is briefly reviewed here with illustrations from studies of two junction models and their dynamical interpretation in the sense of biological bursting.

Smallest Chimeras Under Repulsive Interactions

We present an exemplary system of three identical oscillators in a ring interacting repulsively to show up chimera patterns. The dynamics of individual oscillators is governed by the superconducting Josephson junction. Surprisingly, the repulsive interactions can only establish a symmetry of complete synchrony in the ring, which is broken with increasing repulsive interactions when the junctions pass through serials of asynchronous states (periodic and chaotic) but finally emerge into chimera states. The chimera pattern first appears in chaotic rotational motion of the three junctions when two junctions evolve coherently, while the third junction is incoherent. For larger repulsive coupling, the junctions evolve into another chimera pattern in a periodic state when two junctions remain coherent in rotational motion and one junction transits to incoherent librational motion. This chimera pattern is sensitive to initial conditions in the sense that the chimera state flips to another pattern when two junctions switch to coherent librational motion and the third junction remains in rotational motion, but incoherent. The chimera patterns are detected by using partial and global error functions of the junctions, while the librational and rotational motions are identified by a libration index. All the collective states, complete synchrony, desynchronization, and two chimera patterns are delineated in a parameter plane of the ring of junctions, where the boundaries of complete synchrony are demarcated by using the master stability function.

Extreme multistability in a Josephson-junction-based circuit

We design and report an electrical circuit using a Josephson junction under periodic forcing that reveals extreme multistability. Its overall state equations surprisingly recall those of a well-known model of Josephson junction initially introduced in our circuit. The final circuit is characterized by the presence of two new and different current sources in parallel with the nonlinear internal current source sin[ϕ(t)] of the Josephson junction single electronic component. Furthermore, the model presents an interesting extreme multistability which is justified by a very large number of different attractors (chaotic or not) when slightly changing the initial conditions.

Coherent libration to coherent rotational dynamics via chimeralike states and clustering in a Josephson junction array

An array of excitable Josephson junctions under a global mean-field interaction and a common periodic forcing shows the emergence of two important classes of coherent dynamics, librational and rotational motion, in the weaker and stronger coupling limits, respectively, with transitions to chimeralike states and clustered states in the intermediate coupling range. In this numerical study, we use the Kuramoto complex order parameter and introduce two measures, a libration index and a clustering index, to characterize the dynamical regimes and their transitions and locate them in a parameter plane.

Dynamics of bow-tie shaped bursting: Forced pendulum with dynamic feedback

A detailed study is performed on the parameter space of the mechanical system of a driven pendulum with damping and constant torque under feedback control. We report an interesting bow-tie shaped bursting oscillatory behaviour, which is exhibited for small driving frequencies, in a certain parameter regime, which has not been reported earlier in this forced system with dynamic feedback. We show that the bursting oscillations are caused because of a transition of the quiescent state to the spiking state by a saddle-focus bifurcation, and because of another saddle-focus bifurcation, which leads to cessation of spiking, bringing the system back to the quiescent state. The resting period between two successive bursts (T_rest) is estimated analytically.