Complex dynamics in Josephson system with two external forcing terms

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

“…(20). Therefore, curves (21) and (22) together with Ω 2 − 3B 2 = 0 divide the (Ω, f 2 ) plane into regions (I), (II) and (III), which are shown in Fig.2 (P1). In region (I), Ω < √ 3B and f 2 > f 2 2 ; In region (II), Ω < √ 3B and f 2 1 < f 2 < f 2 2 ; In region (III), Ω < √ 3B and f 2 < f 2 1 .…”

“…By the analysis of the fixed points and their stabilities of (4), we can obtain the following results (see [8,21]). Lemma 2 [8,21] .…”

“…This paper is organized as follows. In Section 2, we briefly describe the fixed points and phase portraits for the unperturbed system of (1) which have proposed in [21]. In Section 3, the analytical results for the bifurcation of harmonics, subharmonics, superharmonics are presented.…”

“…Xu and Jing [20] have transformed the Josephson system into some polynomial systems in some intervals and then the analytic forms of the heteroclinc orbits are obtained and the chaotic regions are discussed by theoretical method. The Josephson system with two periodic forced terms are investigated by Yang, et al [21] who proved the existence of chaos under periodic perturbation by applying Melnikov method and quasi-periodic perturbation by the second-order averaging method and Melnikov method in its averaged system.…”

Heteroclinic orbits and chaotic regions for Josephson system

“…Furthermore, Josephson system (1) is a nonlinear system which exhibits rich dynamical behaviors such as bifurcation, periodic orbit, chaos. Hence many physicists and mathematicians have focused on discussing the dynamics of Josephson system (1) [1][2][3]12,15,17].…”