Static Magnetic Flux Dynamics in One-Dimensional (1D) Josephson Lattices

We investigated static magnetic flux dynamical properties of one-dimensional lattices of Josephson junctions. The discretized wave equations of the Josephson junction lattice were solved using a generalized relaxation iteration algorithm. Numerical simulations indicated that transitions between periodic state and chaotic state will occur as the physical parameters and geometric parameters such as external current y_n, magnetic field h₀, h, and the length of Josephson junction _n and d_n, varied. A shot length of the Josephson junction favors stable periodic states.