A mathematical model for the dynamics of happiness

Positive psychology recognizes happiness as a construct comprising hedonic and eudaimonic well-being dimensions. Integrating these components and a set of theory-led assumptions, we propose a mathematical model, given by a system of nonlinear ordinary differential equations, to describe the dynamics of a person's happiness over time. The mathematical model offers insights into the role of emotions for happiness and why we struggle to attain sustainable happiness and tread the hedonic treadmill oscillating around a relative stable level of well-being. The model also indicates that lasting happiness may be achievable by developing constant eudaimonic emotions or human altruistic qualities that overcome the limits of the homeostatic hedonic system; in mathematical terms, this process is expressed as distinct dynamical bifurcations. This mathematical description is consistent with the idea that eudaimonic well-being is beyond the boundaries of hedonic homeostasis.

Automated summary

This article proposes a mathematical model to describe the dynamics of an individual's happiness over time. The model reveals the role of emotions in happiness and explains why it is difficult to achieve sustainable happiness. The results suggest that lasting happiness can be achieved by cultivating persistent positive emotions or overcoming the limitations of the happiness system.