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In this paper, a logistic oscillator model is presented to analyze the economic cycles of five selected economies: Mexico, Brazil, Canada, China and the United States. This selection was made taking as reference their level of economic development and their geographical position. The proposed model is an extension of the production Phillip's model (1959), which considers autonomous expenses dependent on time. It should be noted that the logistic oscillator combines the dynamics of a forced damped oscillator, whose restoring force incorporates Verhulst's logistic equation. The data used are the production levels of The Organization for Economic Cooperation and Development (OECD) at nominal prices of the mentioned nations. The results obtained show terms of no economic damping with explosive tendency. China shows greater nondamping with an explosive trend, as does Mexico. The countries with the greatest oscillatory behavior are Brazil and Canada. Additionally, those showing exponential dynamics are China and the USA. The fitting of the logistic oscillator to the data is significant given the level of the determination coefficient. Therefore, the results indicate that the model can be useful in formulating economic policy criteria, since it allows one to predict the evolution of the economic cycle in the future. [ABSTRACT FROM AUTHOR]