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

This article discusses the search procedure for Poincaré 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.

Limit sets in product of semi-dynamical

Continuing the study of the properties of Poisson stability and distality [4], we mention the conditions under whichΩx(x)=ΠΩα(xα),α∈Iand thus, the product of Poisson stable motions remains Poisson stable in the product system.

Poisson stability in product of dynamical systems

This paper deals with Poisson stable and distal dynamical system. It is shown that the product of Poisson stable motions is a Poisson stable motion in dynamical systems.