We investigate the diffusion of a particle subjected to a non-sinusoidal periodic potential and driven by an external constant force. To study the dynamic of the Brownian particles, we modify the shape of the potential as well as the temperature. This allows us to observe the dependence of the mean square displacement on the shape parameter as well as the diffusion coefficient. For a particular set of the system parameters, the dispersion-less transport, normal diffusion and hyperdiffusion are generated in the system. We show that there exists a potential shape where some parameters of the system weakly affect the type of diffusion. The diffusion coefficient reaches its maximum around a critical value of the external field. This pronounced peak of the diffusion coefficient depends on the shape of the potential, so we have evaluated the critical force as a function of the potential features.
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