## Solver for Rinaldi's "Laura and Petrarch" Model

Warren Weckesser

 This web page allows you to solve the system of differential equations created by Sergio Rinaldi to model the dynamics of unrequited love between the poet Petrarch and his muse Laura ("Laura and Petrarch: An Intriguing Case of Cyclical Love Dynamics", SIAM J. Appl. Math, Vol. 58, No. 4, pp. 1205-1221, August 1998). The equations solved here are given in equations (6), (7) and (8) on page 1210 of the paper. The default parameter values are given on page 1212 of the paper. With these parameters, the solution plotted here recreates the upper plot of Figure 3 in the paper (page 1214).

Enter the following data, select the Output Options, then click on Show Solution below.

 α1,2,3 = β1,2,3 = γ = δ = AL = AP =

Initial conditions:
 L(0) = P(0) = Z(0) =

Duration of solution: (Maximum duration is 1000.)

Output Options

Phase Space Plots

 Plot Horizontal Axis Vertical Axis L P Z L P Z L P Z L P Z L P Z L P Z

Time Series Plots

 Plot Vertical Axis L P Z L P Z L P Z