Special Seminar in Applied Mathematics

A Degree of Nonlinearity (DN) based primarily on intra-wave frequency modulation is proposed here with the value always between 0 and 1.  With this definition, the degree of nonlinearity would measure the state rather than a system.  The data needed for the definition is just the state of the motion, or observed data.  For a complicate state with more than one IMF containing prominent energy density, the degree of nonlinearity have also considered the amplitude variations.  The combination of both intra-wave frequency modulation and amplitude variation gives the Combined Degree of Nonlinearity (CDN). Extensive tests with known nonlinear system indicate that the new definition is logical and the values of DN given, reasonable.  With these definitions of degree of nonlinearity, we could quantify nonlinearity in the future; then, the discussion of nonlinear effects could be conducted more precisely.