Can a Mathematical Model for a Complex System Do without Environmental Noise?

Davide Valenti

Two examples of complex systems, described by stochastic nonlinear models, are investigated: i) a marine ecosystem whose dynamics is described by a 0-dimensional stochastic variant of the well-known biogeochemical flux model [1]; ii) a financial market described by a nonlinear Heston model [2]. In the first system, data on solar irradiance, collected from the sea surface, are used to model the stochastic dynamics of the ecosystem. The coefficient of variation (a proxy of the variance) displays a nonmonotonic behaviour vs noise intensity, indicating a noise-driven transition of the ecosystem to a non-equilibrium steady state. In the second system, the dynamics of a financial market is investigated by exploiting the mean first hitting time as an indicator of price stability. Specifically, the daily returns of 1,071 stocks traded in the New York Stock Exchange are analyzed, revealing a nonmonotonic behaviour, with a maximum, of the mean first hitting time vs volatility. Finally, a nonlinear Heston model, numerically solved, is used to reproduce this nonmonotonic behavior.

References

[1] R. Grimaudo, P. Lazzari, C. Solidoro, DV, Effects of solar irradiance noise on a complex marine trophic web, Sci. Rep. 12, 12163 (2022).

[2] DV, G. Fazio, B. Spagnolo, Stabilizing effect of volatility in financial markets, Phys. Rev. E 97, 062307 (2018)."