Universal scaling property in bifurcation structure of Duffing's and of generalized Duffing's equations

Abstract

Computer calculation for the numerical solution of Duffing's and generalized Duffing's equations shows global scaling properties for the bifurcation in parameter space. These scaling properties are discussed in terms of a one-dimensional map. The analysis based on a piecewise linear approximation gave results in good agreement with the experimentally observed scaling behavior.