Adequacy of Interpretation of Monitoring Data on Biophysical Processes in Terms of the Theory of Bifurcations and Chaotic Dynamics
Inna Trofimova, A. Yu. Perevaryukha, А. Б. Манвелова
Abstract
Abstract The problem of confirming the correspondence of the dynamics of biophysical processes arising from the incomplete and noisy data obtained during monitoring of the state of bioresources or statistics gathering in a series of laboratory experiments to three behavioral modes of paths of discrete dynamic systems (equilibrium, limiting cycle, or chaos) is considered. It is shown using the examples of real monitoring data and results of laboratory experiments that the data-approximation technique yields a dependence function, which excludes the observed qualitative development of the population process. Attempts to plot regression lines based on the monitoring data for dissipative paths do not yield the necessary information. Known models of biophysics with qualitative changes in the behavior are considered that use characteristics of the reproductive function that cannot be interpreted in terms of the environmental role. The Schwartz derivative depends on the third derivative of the second iteration of the function at the moment of stationary-point stability loss. Criteria for discrete dynamic systems are proposed that can be used to analyze the results of computational simulation from the point of view of biophysical adequacy of occurring nonlinear effects. It is suggested that the rate of population change in the model has a range of negative values and the population reproduction curve has at least two nontrivial stationary points. Consideration of the effect of an aggregated group, arising during invasions, in the action models facilitates an essential interpretation of the behavior of the model path. It is proposed to delimit the nonlinear effects arising in discrete iterative models. In the case of an invasive species that has penetrated into the ecosystem and caused the depletion of its vital resources, a rapid transition to collapse of the new population is possible. Our approach with two-attractor models makes it possible to predict the state of a critically low population of an aggressive intruder.