Search results for "self-excited attractors"
showing 2 items of 2 documents
Hidden and self-excited attractors in radiophysical and biophysical models
2017
One of the central tasks of investigation of dynamical systems is the problem of analysis of the steady (limiting) behavior of the system after the completion of transient processes, i.e., the problem of localization and analysis of attractors (bounded sets of states of the system to which the system tends after transient processes from close initial states). Transition of the system with initial conditions from the vicinity of stationary state to an attractor corresponds to the case of a self-excited attractor. However, there exist attractors of another type: hidden attractors are attractors with the basin of attraction which does not have intersection with a small neighborhoods of any equ…
On lower-bound estimates of the Lyapunov dimension and topological entropy for the Rossler systems
2019
In this paper, on the example of the Rössler systems, the application of the Pyragas time-delay feedback control technique for verification of Eden’s conjecture on the maximum of local Lyapunov dimension, and for the estimation of the topological entropy is demonstrated. To this end, numerical experiments on computation of finite-time local Lyapunov dimensions and finite-time topological entropy on a Rössler attractor and embedded unstable periodic orbits are performed. The problem of reliable numerical computation of the mentioned dimension-like characteristics along the trajectories over large time intervals is discussed. peerReviewed