Petrarch's Canzoniere: Rational addiction and amorous cycles

The paper is concerned with a celebrated collection of love poems, the 14th century Italian poet Francis Petrarch's Canzoniere. A striking feature of these poems is the emotional ups and downs experienced by Petrarch and his platonic mistress Laura. Recently, attempts have been made to model these e motional swings by catastrophe theory or nonlinear differential equations. This paper takes a different approach. Starting with a pair of differential equations that model the dynamics of the emotions of the two individuals, we formulate an optimal control problem. A key hypothesis of this problem i s that Petrarch was a rational addict of his desire for Laura. With specifi c functional forms and parameter values we identify a stable limit cycle th at gives a representation of the oscillating emotions of Laura and Petrarch .