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Fractional-order dynamical models of love. (English) Zbl 1133.91539
Summary: This paper examines fractional-order dynamical models of love. It offers a generalization of a dynamical model recently reported in the literature. The generalization is obtained by permitting the state dynamics of the model to assume fractional orders. The fact that fractional systems possess memory justifies this generalization, as the time evolution of romantic relationships is naturally impacted by memory. We show that with appropriate model parameters, strange chaotic attractors may be obtained under different fractional orders, thus confirming previously reported results obtained from integer-order models, yet at an advantage of reduced system order. Furthermore, this work opens a new direction of research whereby fractional derivative applications might offer more insight into the modeling of dynamical systems in psychology and life sciences. Our results are validated by numerical simulations.
MSC:
91D30Social networks
26A33Fractional derivatives and integrals (real functions)
34C60Qualitative investigation and simulation of models (ODE)