Spiking and Bursting in Josephson Junction

Dana, Syamal K.; Sengupta, Dipendra C.; Hu, Chin–Kun

doi:10.1109/tcsii.2006.882183

Cited by 61 publications

(39 citation statements)

References 25 publications

(43 reference statements)

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“…The chaotic behavior is illustrated in Figure 5 for a specific value of dc bias current . From Figure 5, we observe that system (3a)-(3c) exhibits chaotic attractor similar to the one found in the NRCLSJ model [12][13][14][15][16]. For = 1.25, = 0.707, and = 0.06, we plot the bifurcation diagram depicting the local maxima of ( ) and the largest Lyapunov exponent of system (3a)-(3c) versus the parameter as shown in Figure 6.…”

Section: Dynamical Behaviors Of the Linearsupporting

confidence: 56%

“…For = 0.01, the periodic bursting is observed in Figure 2(d) when the dc bias current and other parameters are kept fixed as for regular spiking. Such spiking behaviors have been found in the NRCLSJ model [16] and are typical of the mammalian neocortex [27]. As in the NRCLSJ model, the LRCLSJ model behaves as a relaxation oscillator for large value of parameter [15].…”

Section: Dynamical Behaviors Of the Linearsupporting

confidence: 52%

“…Regular spiking, intrinsic bursting, and fast spiking which are usually seen in the mammalian neocortex have been found in the NRCLSJ model [15]. For large inductance, the NRCLSJ model behaves as a relaxation oscillator [16]. The NRCLSJ model [8,9] is used to simulate JJ, resulting in a fairly good agreement with experiment.…”

Section: Introductionmentioning

confidence: 76%

See 2 more Smart Citations

Analysis of a No Equilibrium Linear Resistive-Capacitive-Inductance Shunted Junction Model, Dynamics, Synchronization, and Application to Digital Cryptography in Its Fractional-Order Form

et al. 2017

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A linear resistive-capacitive-inductance shunted junction (LRCLSJ) model obtained by replacing the nonlinear piecewise resistance of a nonlinear resistive-capacitive-inductance shunted junction (NRCLSJ) model by a linear resistance is analyzed in this paper. The LRCLSJ model has two or no equilibrium points depending on the dc bias current. For a suitable choice of the parameters, the LRCLSJ model without equilibrium point can exhibit regular and fast spiking, intrinsic and periodic bursting, and periodic and chaotic behaviors. We show that the LRCLSJ model displays similar dynamical behaviors as the NRCLSJ model. Moreover the coexistence between periodic and chaotic attractors is found in the LRCLSJ model for specific parameters. The lowest order of the commensurate form of the no equilibrium LRCLSJ model to exhibit chaotic behavior is found to be 2.934. Moreover, adaptive finite-time synchronization with parameter estimation is applied to achieve synchronization of unidirectional coupled identical fractional-order form of chaotic no equilibrium LRCLSJ models. Finally, a cryptographic encryption scheme with the help of the finite-time synchronization of fractional-order chaotic no equilibrium LRCLSJ models is illustrated through a numerical example, showing that a high level security device can be produced using this system.

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Section: Dynamical Behaviors Of the Linearsupporting

confidence: 56%

Section: Dynamical Behaviors Of the Linearsupporting

confidence: 52%

See 1 more Smart Citation

Analysis of a No Equilibrium Linear Resistive-Capacitive-Inductance Shunted Junction Model, Dynamics, Synchronization, and Application to Digital Cryptography in Its Fractional-Order Form

et al. 2017

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“…This circuit reproduce the neuronal electrical activity [8], [10], [15]. In this work we controlled the RCLSJ circuit for simulate the dynamic properties of the neuronal model showed by Hodgking and Huxley, obtaining coupling function using an improved adaptive track scheme, and this could be understood like the synchronization between two different dynamical system.…”

Section: Introductionmentioning

confidence: 99%

Neuronal Synchronization of Electrical Activity, Using the Hodgkin-Huxley Model and RCLSJ Circuit

Téquita

Naranjo

2016

ing.cienc.

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We simulated the neuronal electrical activity using the Hodgkin-Huxley model (HH) and a superconductor circuit, containing Josephson junctions. These HH model make possible simulate the main neuronal dynamics characteristics such as action potentials, firing threshold and refractory period. The purpose of the manuscript is show a method to syncronize a RCLshunted Josephson junction to a neuronal dynamics represented by the HH model. Thus the RCLSJ circuit is able to mimics the behavior of the HH neuron. We controlated the RCLSJ circuit, using and improved adaptative track scheme, that with the improved Lyapunov functions and the two controllable gain coefficients allowing synchronization of two neuronal models. Results will provide the path to follow forward the understanding neuronal networks synchronization about, generating the intrinsic brain behavior. Sincronización de la actividad eléctrica neuronal, utilizando el modelo de Hodgkin-Huxley y el circuito RCLSJ ResumenSimulamos la actividad eléctrica neuronal mediante el modelo de HodgkinHuxley (HH) y un circuito superconductor, que contiene uniones Josephson. El modelo HH simulan las características principales de la dinámica neuronal tales como potenciales de acción, umbrales de disparo y el perío-dos refractarios. El propósito del manuscrito es mostrar un método para sincronizar un circuito con union Josephson RCLSJ a una dinámica neuronal representado por el modelo HH. Así, el circuito RCLSJ es capaz de imitar el comportamiento de la neurona HH. Controlamos el circuito RCLSJ, utilizando un esquema de control adaptativo, que con funciones de Lyapunov y dos coeficientes de ganancia controlables nos permiten la sincronización de los dos modelos neuronales. Los resultados proporcionan una ruta a seguir adelante en el entendimiento de la sincronización de redes neuronales, generadas por el comportamiento intrinseco del cerebro.Palabras clave: método modelo de Hodgkin-Huxley; uniones Josephson; funciones de Lyapunov; analisis númerico.

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“…Synchronization of the superconducting junction arrays is important for the purpose of generating reasonably large output power [13]. Also, chaos synchronization in superconducting Josephson junction of parallel array of coupled Josephson junctions linked together by inductors has been used in the fabrication of high sensitive detectors [14,15,16].…”

Section: Introductionmentioning

confidence: 99%

Compound-combination synchronization of chaos in identical and different orders chaotic systems

Ojo

Njah

Olusola

2015

Archives of Control Sciences

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This paper proposes a new synchronization scheme called compound-combination synchronization. The scheme is investigated using six chaotic Josephson junctions evolving from different initial conditions based on the drive-response configuration via the active backstepping technique. The technique is applied to achieve compound-combination synchronization of: (i) six identical third order resistive-capacitive-inductive-shunted Josepshon junctions (RCLSJJs) (with three as drive and three as response systems); (ii) three third order RCLSJJs (as drive systems) and three second order resistive-capacitive-shunted Josepshon junctions (RCSJJs (as response systems). In each case, sufficient conditions for global asymptotic stability for compound-combination synchronization to any desired scaling factors are achieved. Numerical simulations are employed to verify the feasibility and effectiveness of the compound-combination synchronization scheme. The result shows that this scheme could be used to vary the junction signal to any desired level and also give a better insight into synchronization in biological systems wherein different organs of different dynamical structures and orders are involved. The scheme could also provide high security in information transmission due to the complexity of its dynamical formulation.Keywodrs: control and applications of chaos, low-and high-dimensional chaos, numerical simulations of chaotic models, synchronization, coupled oscillators.

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Spiking and Bursting in Josephson Junction

Cited by 61 publications

References 25 publications

Analysis of a No Equilibrium Linear Resistive-Capacitive-Inductance Shunted Junction Model, Dynamics, Synchronization, and Application to Digital Cryptography in Its Fractional-Order Form

Analysis of a No Equilibrium Linear Resistive-Capacitive-Inductance Shunted Junction Model, Dynamics, Synchronization, and Application to Digital Cryptography in Its Fractional-Order Form

Neuronal Synchronization of Electrical Activity, Using the Hodgkin-Huxley Model and RCLSJ Circuit

Compound-combination synchronization of chaos in identical and different orders chaotic systems

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