Abstract: Based on the cusp-catastrophe model of nonlinear theory, this paper examines the influence of water flow conditions and the relative position of sediment particles on riverbed on the nonlinear dynamic characteristics of sediment transport, formulates the state variables and control variables of this model, and constructs a new cusp-catastrophe model for qualitative description of bedload transport. Through coordinate transformation and topological transformation, a nonlinear bedload transport rate formula is derived. This formula is verified against previous measurements and compared with other formulas of the same theory and the classical formulas. We explain the difference in calculations of low-intensity sediment transport using different formulas, and present an analysis on the cause of sudden changes in the calculation accuracy of high-intensity sediment transport. And the influence of incipient shear stress of bedload motions on the formula of sediment transport rate is discussed. It is verified that our nonlinear formula is reasonable with good applicability.

Key words: nonlinearity, cusp-catastrophe model, incipient motion parameter, variable analysis, topological transformation, bedload sediment transport