A mathematical model for the dynamics of happiness

Gustavo Carrero, Joel Makin, Peter Malinowski

Research output: Contribution to journalJournal Articlepeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)2002-2029
Number of pages28
JournalMathematical Biosciences and Engineering
Issue number2
Publication statusPublished - 2022


  • Eudaimonic well-being
  • Happiness model
  • Hedonic well-being
  • Lasting happiness
  • Mathematical bifurcations


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