Stabilization and complex dynamics initiated by pulsed force in the Rössler system near saddle-node bifurcation

Nonlinear Dynamics. 2024. Vol. 112. No. 4. P. 2949–2967.

Stankevich N.

Stabilization by a periodic pulsed force of trajectories running away to infinity in the three-dimensional R ̈ossler system at a threshold of a saddle-node bifurcation, birth of equilibrium states is studied. It is shown that the external pulsed action stabilizes dynamical regimes in a fairly wide range of external signal parameters. Stabilized regimes can be periodic, quasi-periodic, or chaotic. Three types of chaotic oscillations are revealed depending on the spectrum of Lyapunov exponents: the simplest (classical) and multi- dimensional (hyperchaos and chaos with additional zero Lyapunov exponent). Scenarios for the development of multi-dimensional chaos have been studied in detail. The universality of the observed behavior when chang- ing the direction of the external force is investigated. It is shown that the effects are universal, when force acts in a plane corresponding to focal behavior of the trajectories, stabilization is not observed if the direction of force is perpendicular to the plane. The universality of the obtained picture is studied when the autonomous dynamics of the model change, it is shown that for small periods of external action, the picture is determined by a transient processes of autonomous model and remains characteristic for stabilization. With an increase in the period of external force, the properties of an autonomous model appear.

Keywords: stabilization, chaos, Lyapunov exponents, quasiperiodic oscillations, hyperchaos, Pulsed force

Publication based on the results of: Развитие аналитических и численных методов исследования многомерных динамических систем: этап I (2023)