Determinism versus randomness in plankton dynamics: The analysis of noisy time series based on the recurrence plots

Abstract

Abstract The quantitative analysis of recurrence plots while applied to mathematical models was shown to be an effective tool in recognizing a frontier between deterministic chaos and random processes. In nature, however, unlike mathematical models, deterministic processes are closely intertwined with random influences. As a result, the non-structural distributions of points on the recurrence plots, which are typical of random processes, are inevitably superimposed on the aperiodic structures characteristic of chaos. Taking into account that the stochastic impacts are an inherent feature of the dynamics of populations in the wild, we present here the results of the analysis of recurrence plots in order to reveal the extent to which irregular phytoplankton oscillations in the Naroch Lakes, Belarus, are susceptible to stochastic impacts. We demonstrate that numerical assessments of the horizon of predictability Tpr of the dynamics under study and the average number Pd of the points that belong to the diagonal segments on the recurrence plots can furnish insights into the extent to which the dynamics of both model and phytoplankton populations are affected by random components. Specifically, a comparative analysis of the values of Tpr and Pd for the time series of phytoplankton and the time series of random processes allows us to conclude that random components of the phytoplankton dynamics in the Naroch Lakes do not prevent recognition of chaotic nature of these dynamics.