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

Abstract

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.

Dynamical Analysis and Microcontroller Implementation of Linear Resistor-Capacitor Shunted Josephson Junction Model

“…Nonetheless, it was not able to generate significant features of experimental currentvoltage characteristics. Better agreement with experiment is found when the RCSJJ model is adopted by inserting an inductor in series with the shunt resistor in order to obtain the RCLSJJ model (Cawthorne et al 1998;Dana et al 2006;Whan et al 1995;Stewart 1968;Neumann and Pikovsky 2003;Takougang Kingni et al 2017).…”

“…In fact, there is four models of JJ namely: Nonlinear RCSJJ model (Levi et al 1978;Likharev 1986), LRCSJJ model (Salam and Sastry 1985;Bartuccelli et al 1986),nonlinear RCLSJJ model (Cawthorne et al 1998;Dana et al 2006;Whan et al 1995;Stewart 1968), and linear RCISJJ model (Neumann and Pikovsky 2003;Takougang Kingni et al 2017) have been reviewed to check if a JJ device can be used as a transmitter and receiver in chaos based communications. The two RCSJJ models show chaotic behaviors when driven by external sinusoidal current source (Levi et al 1978;Likharev 1986;Salam and Sastry 1985;Bartuccelli et al 1986) whereas the two RCISJJ models generated chaotic behaviors with external DC (Cawthorne et al 1998;Dana et al 2006;Whan et al 1995;Stewart 1968;Neumann and Pikovsky 2003;Takougang Kingni et al 2017;Dana et al 2001).The RCISJ models have been revealed more appropriate in high-frequency applications (Cawthorne et al 1998;Dana et al 2006;Whan et al 1995;Stewart 1968;Neumann and Pikovsky 2003;Takougang Kingni et al 2017). In (Dana et al 2006), Dana et al have been studied how the chaos found in nonlinear RCLSJJ model could be applied as a chaos generator for communications.…”

Microcontroller Implementation, Chaos Control, Synchronization and Antisynchronization of Josephson Junction Model

“…It has been found that the NRCSJJ and LRCSJJ models show chaotic behaviors when they are driven by an external sinusoidal signal [14]. In comparison, the LRCISJJ and NRCISJJ models can generate chaotic behaviors with external DC bias [17][18][19]. The NRCISJJ and LRCISJJ models significantly reproduce the features on experimental curves than NRCSJJ and LRCSJJ models [17,22,23].…”

“…Many models have been used to study, characterize and represent the JJ properties. These include the nonlinear resistive-capacitive shunted JJ (NRCSJJ) model, the linear resistive-capacitive shunted JJ (LRCSJJ) model, linear resistive-capacitive-inductive shunted JJ (LRCISJJ) model [11][12][13], the nonlinear resistive-capacitive-inductive shunted JJ (NRCISJJ) model [14][15][16][17][18][19][20] autonomous Josephson jerk oscillator [15], and a single mesh JJ [16] just to name a few. It has been found that the NRCSJJ and LRCSJJ models show chaotic behaviors when they are driven by an external sinusoidal signal [14].…”

“…Many works showing multiples attractors phenomena have been carried out in the literature, in particular, Infinite attractors in a chaotic circuit with exponential memristor and JJ resonator [21]. In [18], it has been demonstrated that the LRCISJJ model can exhibit hidden chaotic attractors and the coexisting attractors between periodic and hidden chaotic attractors for a suitable choice of the parameters. In this paper, a microcontroller implementation is used to confirm the existence of different shapes of hidden chaotic attractors found in the NRCISJJ model during the numerical simulations.…”