Chaos and bifurcation in Josephson voltage-controlled oscillators

Smith, Andrew D.; Sandell, R.; Silver, A. H.; Burch, J.F.

doi:10.1109/tmag.1987.1064914

Cited by 11 publications

(3 citation statements)

References 4 publications

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“…The NRCLSJ model [8,9] is used to simulate JJ, resulting in a fairly good agreement with experiment. The RCSJ model, however, fails to reproduce significant features on experimental -curves when the shunt of the JJ contains an inductance component [12,17].…”

Section: Introductionmentioning

confidence: 96%

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: Introductionmentioning

confidence: 96%

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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“…In the nonlinear consideration, the RCLSJJO exposes better agreement between simulations and experimentation [23,24], and considering extreme inductance, the RCLSJJO exhibits similar properties to the relaxation oscillator [25,26]. The limitation in both investigation and application concerning the resistive capacitive shunted JJ circuits exhibiting insignificant characteristics regarding the I-V plots experimentally [5,27,28] has subjected increasing consideration on the RCLSJJO. Though the RCLSJJO was not considered extensively regarding the literature of the JJ, its vast uses and technological integration have subjected the circuit design to increasing research findings.…”

Section: Introductionmentioning

confidence: 99%

Josephson junction oscillator embedded in the microcontroller: Pseudo-random number generation and combination synchronization

Sriram,

Awilo,

Donald Dongmo

et al. 2023

Phys. Scr.

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Dynamical scrutiny of the resistive capacitive inductive shunted Josephson junction (JJ) oscillator (RCLSJJO), microcontroller realization, pseudo-random number generation (PRNG) and combination synchronization are achieved in this paper. Numerical probing led to the establishment that the RCLSJJO is characterized by regular behaviors, bistable periodic-2-oscillations, periodic bursting characteristics and various shapes of chaotic dynamics. Thereafter, the vast dynamical characteristics obtained theoretically are realized by the microcontroller realization with qualitative agreements. Moreover, a chaos-based PRNG is designed by using chaotic RCLSJJO and linear feedback shift register (LFSR) as post-processing unit. Satisfactory results are obtained from the NIST 800–22 test suite and the randomness of binary data generated from the proposed RCLSJJO-based PRNG is confirmed for chaos-based digital applications. Lastly, the combination chaos synchronization of two drive and one response RCLSJJO is proven thanks to the theoretical analysis.

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“…!-4 Previously, Josephson parametric amplifiers were, during several years, cursed by high-noise temperatures,5-.15 the cause of which was not fully understood. [35][36][37][38][39][40][41][42] This work will show that it is possible to obtain stable oscillations and low-noise amplification over a sizeable bandwidth in resistive rfSQUIDs if the circuit elements and the operation parameters are carefully controlled and the device is impedance matched to the outside world. [16][17][18][19][20][21][22][23][24][25] Several extensive theoretical investigations have been made to characterize Josephson junction parametric amplifiers.…”

Section: T Introductionmentioning

confidence: 99%

Low-noise Josephson parametric amplification and oscillations at 9 GHz

Olsson

Claeson

1988

Journal of Applied Physics

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We have investigated the performance of a resistive rf SQUID as a 9 GHz parametric amplifier and oscillator. It was coupled to a low impedance microstrip transformer. Stable Josephson oscillations were obtained for βLQ =2eI0ZL/hf <1.1–1.8. Oscillation linewidth (830 kHz) and output power (−74 dBm) were measured. The four-photon internally pumped amplifier produced large single sideband (ssb) noise temperatures, typically around 50 K, due to the broad flanks of the pump. The best performance was achieved in the three- and four-photon externally pumped modes. Both modes gave signal gains of about 10 dB and negligible noise power contributions. A hot/cold measurement on the four-photon amplifier yielded Gdsb =13 dB (dsb=double sideband) and Tdsb =3±4 K over a bandwidth of 310 MHz. For larger values of βLQ , subharmonics 1/2 and 1/3, as well as noninteger ‘‘excitations’’ of the Josephson oscillation, were observed. The subharmonic oscillations were not tunable in frequency with unchanged linewidth. Amplification close to an excitation also produced gain but with ssb noise temperatures of ∼20 K.

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Chaos and bifurcation in Josephson voltage-controlled oscillators

Cited by 11 publications

References 4 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

Josephson junction oscillator embedded in the microcontroller: Pseudo-random number generation and combination synchronization

Low-noise Josephson parametric amplification and oscillations at 9 GHz

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