In the present work we reconsider the evolutionary game theoretic models by Antoci et al. (2016, 2018) describing the dynamic outcomes arising from the interactions between patients and physicians, whose behavior is subject to clinical and legal risks. In particular, Antoci et al. (2016) analyzed the case of positive defensive medicine, while Antoci et al. (2018) dealt with the case of negative defensive medicine. We show that, when the models admit a nonisochronous center, it is possible to prove the existence of chaotic dynamics for the Poincaré map associated with those systems via the method of Linked Twist Maps (LTMs). To such aim we exploit in both frameworks, using a similar rationale, the periodic dependence on time of a model parameter influencing the position of the center and describing some risk associated with certain medical interventions, whose seasonal variation is empirically grounded. We also recall the ecological interpretation of the same model proposed by Harvie et al. (2007) and connected with intraspecific competition and environmental carrying capacity in predator-prey settings. In this case, it is sensible to assume a seasonal variation both for the carrying capacities and for the intrinsic growth rates of the two populations. Although such parameters influence the shape of the orbits, but do not affect the center position, we show that it is still possible to prove the existence of chaotic dynamics for the associated Poincaré map via the LTMs technique dealing with a different geometrical configuration for orbits in the phase plane.

Pireddu, M. (2021). Chaotic dynamics in the presence of medical malpractice litigation: A topological proof via linked twist maps for two evolutionary game theoretic contexts. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 501(2 (15 September 2021)) [10.1016/j.jmaa.2021.125224].

Chaotic dynamics in the presence of medical malpractice litigation: A topological proof via linked twist maps for two evolutionary game theoretic contexts

Pireddu, M
2021

Abstract

In the present work we reconsider the evolutionary game theoretic models by Antoci et al. (2016, 2018) describing the dynamic outcomes arising from the interactions between patients and physicians, whose behavior is subject to clinical and legal risks. In particular, Antoci et al. (2016) analyzed the case of positive defensive medicine, while Antoci et al. (2018) dealt with the case of negative defensive medicine. We show that, when the models admit a nonisochronous center, it is possible to prove the existence of chaotic dynamics for the Poincaré map associated with those systems via the method of Linked Twist Maps (LTMs). To such aim we exploit in both frameworks, using a similar rationale, the periodic dependence on time of a model parameter influencing the position of the center and describing some risk associated with certain medical interventions, whose seasonal variation is empirically grounded. We also recall the ecological interpretation of the same model proposed by Harvie et al. (2007) and connected with intraspecific competition and environmental carrying capacity in predator-prey settings. In this case, it is sensible to assume a seasonal variation both for the carrying capacities and for the intrinsic growth rates of the two populations. Although such parameters influence the shape of the orbits, but do not affect the center position, we show that it is still possible to prove the existence of chaotic dynamics for the associated Poincaré map via the LTMs technique dealing with a different geometrical configuration for orbits in the phase plane.
Articolo in rivista - Articolo scientifico
Chaotic dynamics; Hamiltonian system; Linked twist maps; Nonisochronous center; Periodic coefficients; Seasonal effect;
English
2-apr-2021
2021
501
2 (15 September 2021)
125224
partially_open
Pireddu, M. (2021). Chaotic dynamics in the presence of medical malpractice litigation: A topological proof via linked twist maps for two evolutionary game theoretic contexts. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 501(2 (15 September 2021)) [10.1016/j.jmaa.2021.125224].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/310394
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