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Logarithmic oscillations superimposed on a power-law trend appear in thebehavior of various complex hierarchical systems. In this paper, we study thelogarithmic oscillations of relaxation curves in p-adic diffusion models thatare used to describe the conformational dynamics of protein. We consider thecase of a purely p-adic diffusion, as well as the case of p-adic diffusion witha reaction sink. We show that, relaxation curves for large times in these twocases are described by a power law on which logarithmic oscillations aresuperimposed whose period and amplitude are determined by the parameters of themodel. We also provide a physical explanation of the emergence of oscillationsin relaxation curves and discuss the relation of the results to the experimentson relaxation dynamics of protein.

Oscillations in p-adic diffusion processes and simulation of the conformational dynamics of protein