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This article discusses the search procedure for the Poincar\'e recurrences toclassify solutions on an attractor of a fourth-order nonlinear dynamical systemusing a previously developed high-precision numerical method. For the resultinglimiting solution, the Lyapunov exponents are calculated using the modifiedBenettin's algorithm to study the stability of the found regime and confirm thetype of attractor.

On the Poisson Stability to Study a Fourth-Order Dynamical System with Quadratic Nonlinearities