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A mathematical model for the dynamics of happiness


  • Received: 12 September 2021 Accepted: 13 December 2021 Published: 24 December 2021
  • 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.

    Citation: Gustavo Carrero, Joel Makin, Peter Malinowski. A mathematical model for the dynamics of happiness[J]. Mathematical Biosciences and Engineering, 2022, 19(2): 2002-2029. doi: 10.3934/mbe.2022094

    Related Papers:

  • 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.



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