<p>The paper is devoted to a numerical study of a new variety of shock reflection hysteresis in axisymmetrical steady supersonic flow. A converging shock wave produced by a straight ring-wedge impinges on a cylinder placed along the axis of symmetry. The converging axisymmetrical shock gradually steepens as it approaches the surface of the cylinder. It is shown that it is possible to change the incident shock angle and Mach number and traverse the dual-solution domain by expanding and contracting the axial cylinder in a quasi-steady manner. The existence of shock reflection hysteresis induced in such a manner is demonstrated with an unstructured Euler finite-volume flow solver. The values of cylinder radius, and hence incident shock angle, at which regular-to-Mach and Mach-to-regular transitions of the hysteresis loop occur, are determined and compared with the theoretical detachment and von Neumann values.</p>