A.Yu. Perevaryukha1

1 St. Petersburg Federal Research Center of the Russian Academy of Sciences (St. Petersburg, Russia)

Formulation of the problem. We need to determine the features of different biological processes, the specifics of which must be taken into account when choosing a mathematical apparatus for modeling their changes. With the use of functional iterative structures, it is possible to implement a diverse range of trajectory behavior modes and obtain their changes, smooth or rapid. Nowadays, not only ordinary discrete mappings are used, but also their extensions in models based on dynamical systems with a variable evolution operator, the variants of which we proposed earlier.

Target. Identify traits and characteristics for a multivariate iterative population model that can generate redundant nonlinear effects. We cannot compare these effects with the ecological reality, but under other conditions the solutions of the models will be quite explicable.

Results. It is shown that intervals of values with an internal crisis of the attractor can imperceptibly and narrowly wedge into the range of admissible variation of parameters in a computational experiment. It was possible to reveal the existence of parametric ranges for the known models, for which the behavior of the trajectory cannot be properly interpreted in biological problems, and a method for circumventing this problem was proposed.

Practical significance. We have proposed a method for differentiating the parameters of population models that cause bifurcations, presenting them as interval specified values to exclude excessive metamorphoses of the phase portrait by the example of models of the dynamics of fish stock replenishment.

Perevaryukha A.Yu. Parametric intervals of interpretability in iterative models of real ecological processes. Nonlinear World. 2022. V. 20. № 1. P. 55-64. DOI: https://doi.org/10.18127/j20700970-202201-06 (In Russian)

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