Chaotic Oscillations in a Fractional-Order Circuit with a Josephson Junction Resonator and Its Synchronization Using Fuzzy Sliding Mode Control

Abstract

A linear resistive capacitive inductive shunted model of a Josephson junction with a topologically nontrivial behaviour is considered in this paper. We have considered a fractional-order flux-controlled memristor to effectively model the feedback flux effects across the Josephson junction (JJ). The mathematical model of the proposed JJ oscillator is derived, and the dimensionless model is used to study the various dynamical properties of the oscillator. The stability plot shows that the proposed oscillator has both stable and unstable regions of oscillations for different choices of equilibrium points and fractional order. The bifurcation plots are presented to understand the route to crisis, and we have also shown that the oscillator has regions of coexisting attractors. We have also achieved the synchronization of the proposed oscillator using fuzzy sliding mode control with the master and slave systems considered with different parameter sets. The chattering amplitude is estimated by using the fuzzy logic, and it is used in the synchronization algorithm to minimize the error.

Chaotic Vibration Control of a Composite Cantilever Beam

“…Afterwards, a fuzzy sliding mode control (FSMC), based on SMC, was proposed [19][20][21]. Ramakrishnan [22] used FSMC to control chaotic oscillations in a fractional-order circuit synchronously. Rajaei [23] considered the nonlinear vibration control of a nonlocal strain gradient nanobeam, using an adaptive self-organizing FSMC controller.…”

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

“…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. The existing literature on the model and application has been exposed recently by different scholars [21,26,[29][30][31][32][33][34][35], but PRNG and combination synchronization in the model at low critical temperature superconductor is not investigated and remains open. This aspect is interesting as it observed security in communications which is investigated in this research paper.…”

Fractional-Order sliding mode control of a 4D memristive chaotic system

“…Li et al (2011) employed a dynamic sliding surface and formed a chatter-free SMC to control a chaotic system with uncertainties. Fuzzy SMC (Ramakrishnan et al, 2022) and LMI-based SMC (Wang et al, 2009) techniques were utilized to drive the state of nonlinear chaotic systems to defined equilibrium points in the state space. Moreover, further developments in fractional calculus have led some researchers to employ FOSMC in an integer-order chaotic system (Dadras and Momeni, 2012), classical SMC in a fractional-order chaotic system (Yin et al, 2012), or FOSMC in fractional-order chaotic systems (Yang and Liu, 2013; Balasubramaniam and Muthukumar et al, 2015).…”