Petrarch's "Canzoniere": Rational addiction and amorous cycles

Jorgensen SA, Feichtinger G, & Novak A (1999). Petrarch's "Canzoniere": Rational addiction and amorous cycles. Journal of Mathematical Sociology 23 (3): 225-240. DOI:10.1080/0022250X.1999.9990221.

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Abstract

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 emotional 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 is that Petrarch was a rational addict of his desire for Laura. With specific functional forms and parameter values we identify a stable limit cycle that gives a representation of the oscillating emotions of Laura and Petrarch.

Item Type: Article
Uncontrolled Keywords: Differential equations; optimal control theory; addictive behavior; limit cycle; love affairs
Research Programs: World Population (POP)
Bibliographic Reference: Journal of Mathematical Sociology; 23(3):225-240 (1999)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 02:10
Last Modified: 25 Feb 2016 13:43
URI: http://pure.iiasa.ac.at/5740

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