How to embed shrimps in parameter planes of the Lorenz system

Shrimps are typical periodic islands present in chaotic regions of parameter planes of nonlinear dynamical systems. Such periodic structures have been observed in several different fields including mathematical models simulating lasers, electronic circuits, chemical reactions, neural networks, and biological systems. As far as I know the existence of shrimps in parameter planes of the Lorenz system has never been reported. This paper describes how to display such structures embedded in chaotic regions of parameter planes of the Lorenz system. This is accomplished by considering a shift in the x variable of the $\dot{x}$ differential equation. Additionally it is shown that these periodic structures may appear organized in period-adding sequences. (paper)