Love Dynamics: Coupled Equations of Coupling

A simple mathematical model for romantic relationships, to arouse your interest in the classification of fixed points for linear differential equations. Consider Romeo and Juliet in fair Verona, where we lay our scene, and the parameters that determine their possible love-hate relationships.
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References:
Steven Strogatz, "Nonlinear Dynamics and Chaos", Chapter 5: Linear Systems
Chapter 1 of book, "Modeling Love Dynamics" (2015)
Sergio Rinaldi, Fabio Della Rossa, Fabio Dercole, Alessandra Gragnani, and Pietro Landi
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Romeo Juliet Rinaldi romance dynamics love affairs insecure secure love story between Scarlett and Rhett described in ‘‘Gone with the Wind’’ apathy mutual love mutual hate fixed point classification matrix trace matrix determinant complex conjugate eigenvalue pair autonomous on the plane phase plane are introduced 2D ordinary differential equations 2d ODE vector field topology cylinder bifurcation robustness fragility cusp unfolding perturbations structural stability emergence critical point critical slowing down supercritical bifurcation subcritical bifurcations buckling beam model change of stability nonlinear dynamics dynamical systems differential equations dimensions phase space Poincare Strogatz graphical method Fixed Point Equilibrium Equilibria Stability Stable Point Unstable Point Linear Stability Analysis Vector Field Two-Dimensional 2-dimensional Functions Shakespeare tragedy comedy love-hate relationship mathematics of love relationships
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