The in-phase states of Josephson junctions stacks as attractors

The aim of this investigation is to show that the coherent, in-phase states of intrinsic Josephson junctions stacks are attractors of the stacks' states when the applied external magnetic field he and the external current γ vary within certain domains. Mathematically the problem is to find the solutions of the system of perturbed sine-Gordon equations for fixed other parameters and zero or random initial conditions. We determine the region in the plane (he, γ), where the in-phase states are attractors of the stack's states for arbitrary initial perturbations. This is important, because the in-phase states are required for achieving terahertz radiation from the Josephson stacks.