Bifurcations of periodic solutions and chaos in Josephson system with parametric excitation

Abstract

Josephson system with parametric excitation is investigated. Using second-order averaging method and Melnikov function, we analyze the existence and bifurcations for harmonic, (2, 3, n-order) subharmonics and (2, 3-order) superharmonics and the heterocilinic and homoclinic bifurcations for chaos under periodic perturbation. Using numerical simulation, we check our theoretical analysis and further study the effect of the parameters on dynamics. We find the complex dynamics, including the jumping behaviors, symmetrybreaking, chaos converting to periodic orbits, interior crisis, non-attracting chaotic set, interlocking (reverse) period-doubling bifurcations from periodic orbits, the processes from interlocking period-doubling bifurcations of periodic orbits to chaos after strange non-chaotic motions when the parameter β increases, etc.

Trajectory Tracking between Josephson Junction and Classical Chaotic System via Iterative Learning Control

“…Many studies have exhibited the chaotic behavior in superconducting resistive-capacitive-inductance Josephson Junction (RCLs-JJ) systems [2][3][4]. The properties of RCLs-JJ including the homo-clinic, hetero-clinic, and super-harmonic bifurcations have been investigated to be excited by these varying parameters [5]. The damped pendulum equation describes the junction behavior and demonstrates the chaotic strange attractor in the phase space [6].…”