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The efficiency and uniqueness of the diffusive shock acceleration is studiedon the basis of the novel kinetic solutions. These solutions obtained earlier(paper I, astro-ph/9707152) selfconsistently describe a strong coupling ofcosmic rays with the gas flow. They show that the dependence of theacceleration efficiency upon physical parameters is critical in nature. In thispaper we investigate a steady acceleration in the parameter space formed by theinjection rate (\nu ), the upper cut-off momentum p_1 and the Mach number Mwhile the flow compression R serves as an order parameter. We determine amanifold of all possible solutions in this parameter space.Comment: 24 pages, 8 PostScript figures, uses aasms4.sty, to appear in Dec.  20, 1997 issue ApJ, vol. 49

Bifurcation, Efficiency, and the Role of Injection in Shock Acceleration with the Bohm Diffusion