On Math, Muses, and Poets
Three ordinary differential equations are proposed to model the dynamics of love between Petrarch, a celebrated Italian poet of the 14th century, and Laura, a beautiful but married lady. The equations are nonlinear but can be studied through the singular perturbation approach if the inspiration of the poet is assumed to have very slow dynamics. In such a case, explicit conditions are found in the appeals of Laura and Petrarch and in their behavioral parameters that guarantee the existence of a globally stable slow-fast limit cycle. ... The result is that the calibrated model shows that the poet's emotions followed for about 20 years a quite regular cyclical pattern ranging from the extremems of ecstasy to despair. All of these findings agree with the recent results of Frederic Jones, who, through a detailed stylistic and linguistic analysis of the poems inspired by Laura, has discovered Petrarch's emotional cycle in a fully independent way.
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