The study of dynamic characteristics in nonlinear systems

A new algorithm is proposed to calculate the Laplace transform of the product of functions, so that the transformation could be used to solve the problem of nonlinear systems. The nonlinear transfer functions and approximate solutions of pulse response in the first- and second-order systems, which are calculated by this method, are the same as those by the Volterra series method, but could be obtained more conveniently. The frequency responses of first- and second-order systems with cubic nonlinearities and their stability problems are studied. A judgement is proposed for second-order nonlinear systems to prevent some special phenomena of nonlinear systems, such as jump, superharmonic resonance, bifurcation, etc.<
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