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

This article discusses the search procedure for Poincare recurrences to classify solutions on an attractor of a fourth-order nonlinear dynamical system, using a previously developed high-precision numerical method. For the resulting limiting solution, the Lyapunov exponents are calculated, using the modified Benettin's algorithm to study the stability of the found regime and confirm the type of attractor.

Automated summary

This article discusses the search procedure for Poincare recurrences to classify solutions on an attractor of a fourth-order nonlinear dynamical system, using a previously developed high-precision numerical method. The Lyapunov exponents are calculated for the resulting limiting solution, using the modified Benettin's algorithm to study the stability of the found regime and confirm the type of attractor.