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An efficient homotopy-based Poincaré-Lindstedt method for the periodic steady-state analysis of nonlinear autonomous oscillators

The periodic steady-state analysis of nonlinear systems has always been an important topic in electronic design automation (EDA). For autonomous systems, the mainstream approaches, like shooting Newton and harmonic balance, are difficult to employ since the period itself becomes an unknown. This paper presents an innovative state-space homotopy-based Poincaré-Lindstedt method, with a novel Padé approximation of the stretched time axis, that effectively overcomes this hurdle. Examples demonstrate the excellent efficiency and scalability of the proposed approach.