A mathematical model for the dynamics of happiness

Gustavo Carrero; Joel Makin; Peter Malinowski; Gustavo Carrero; Joel Makin; Peter Malinowski

doi:10.3934/mbe.2022094

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 2: 2002-2029. doi: 10.3934/mbe.2022094

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Research article Special Issues

A mathematical model for the dynamics of happiness

1.
Centre for Science, Faculty of Science and Technology, Athabasca University, Edmonton, Canada
2.
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, Australia
3.
Research Centre for Brain and Behaviour, Liverpool John Moores University, Liverpool, United Kingdom

Academic Editor:Enrique Ponce

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.
- happiness model,
- hedonic well-being,
- eudaimonic well-being,
- mathematical bifurcations,
- lasting happiness
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

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Abstract

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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