Abstract
We investigate the remarkable role of position dependent damping in determining the parametric regions of symmetry breaking in nonlinear PT -symmetric systems. In the two dimensional cases of such position dependent damped systems, we unveil the existence of a class of novel bi-PT symmetric systems which have two fold PT symmetries. We analyze the dynamics of these systems and show how symmetry breaking occurs, that is whether the symmetry breaking of the two PT symmetries occurs in pair or occurs one by one. The addition of linear damping in these nonlinearly damped systems induces competition between the two types of damping. This competition results in a PT phase transition in which the PT symmetry is broken for lower loss/gain strength and is restored by increasing the loss/gain strength. We also show that by properly designing the form of the position dependent damping, we can tailor the PT -symmetric regions of the system.
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