Dynamical Models of Love

J. C. Sprott
Department of Physics, University of Wisconsin - Madison


Following a suggestion of Strogatz, this paper examines a sequence of dynamical models involving coupled ordinary differential equations describing the time-variation of the love or hate displayed by individuals in a romantic relationship. The models start with a linear system of two individuals and advance to love triangles and finally to include the effect of nonlinearities, which are shown to produce chaos.

Ref: J. C. Sprott,  Nonlinear Dynamics, Psychology, and Life Sciences 8, 303-313 (2004).

The complete paper is available in PDF format.

See the companion paper on Dynamical Models of Happiness.

A less technical, more personal version of this is in Chapter 18 of my Memoirs.

Return to Sprott's Books and Publications.

Fig 1. Dynamics in the vicinity of an equilibrium point in two dimensions from Eq. 1.

Fig. 2. One solution of the linear love triangle in Eq. 3.

Fig. 3. One solution of the nonlinear Romeo-Juliet dynamic in Eq. 4.

Fig. 4. Strange attractor from the nonlinear love triangle in Eq. 5.

Fig. 5. Chaotic evolution of Romeo's love for Juliet from Eq. 5 showing the effect of changing the initial conditions by 1%.