Abstract
In this paper, we propose a method for the analysis of multidimensional non-linear systems with periodically varying coefficients by means of truncated point mappings. The proposed method, based on multinomial truncation, generates an explicit analytical expression for the point mapping in terms of the states and parameters of the system to any order of approximation. This approach when combined with analytical techniques, such as the perturbation method employed here, forms a powerful tool for the analysis of periodic solutions and their stability. The underlaying principles of point mapping analysis are discussed and an algorithm for generating truncated point mappings for non-linear periodic systems is derived. To demonstrate the proposed method, it is applied to study the periodic solutions of a forced Duffing's equation and for a parametric analysis of periodic solutions of Matheiu's equation.
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