With the burst of a Wanna decryptor [1] in the middle of 2017, secure communication within a network [2] has again
triggered the considerable attention. Meanwhile, many feasible methods have been proposed to enhance the data security
and it is also involved with chaotic encryption, which is one of the important branch of the chaos theory. Come what
may, it is necessary to investigate the dynamical system with chaotic features [3–8] . Therefore, these topics are related
to the systems with hidden attractor, multi-scroll attractor, attractor without equilibrium points, and infinite equilibrium
points [9–20] , the main contribution of these topics could be associated with chaos. Interestingly, chaotic behaviors can
also be generated in the system mapped from the nonlinear circuit composed of the Josephson Junction [21–23] . The effect
of Josephson Junction in superconductors [24–26] has, since its discovery in the 1960s, been the focus of great interest
both due to its implications for fundamental questions in physics and electronics, particularly, where it promised significant
increase in device speed and sensitivity. The most of the distinct effect of Josephson Junction has been an attempt to develop
Josephson Junctions as high-speed (picosecond) switches for digital applications [27] . The emphasis is now shifting to analog
applications and devices [28] , such as the voltage standard, squid magnetometers, millimeter, submillimeter mixers. It did
focus on mathematical techniques for obtaining analytical results by using various models of the Josephson Junction [29]