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On the dynamics of love: a model including synergism. (English) Zbl 1348.34083

Summary: In their paper, entitled “Dynamics of Love and Happiness: A Mathematical Analysis”, D. Satsangi and Arun K. Sinha proposed a dynamical model which described love affairs between two individuals. Similar to Rinaldi’s model, it includes the phenomena of oblivion, return (both described by linear functions) and instinct (supposed constant), but introduces a nonlinear component for each member of the couple, with the meaning of synergism and emotional interaction. The concept is interesting and appears to be more realistic than those models known in the literature; however, unfortunately the stability analysis is wrong. In the present paper we follow their modelling approach to discuss the dynamics of the feelings between two people by proposing a further modification to the original model, and provide corrections to the stability analysis.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
34D20 Stability of solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
91C99 Social and behavioral sciences: general topics
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