• Corpus ID: 244270246

Search for Invariant Sets of the Generalized Tent Map

  title={Search for Invariant Sets of the Generalized Tent Map},
  author={Kimberly Ayers and Dmitry Dmitrishin and Ami Radunskaya and Alexander M. Stokolos and Constantine Stokolos},
This paper describes a predictive control method to search for unstable periodic orbits of the generalized tent map. The invariant set containing periodic orbits is a repelling set with a complicated Cantor-like structure. Therefore, a simple local stabilization of the orbit may not be enough to find a periodic orbit, due to the small measure of the basin of attraction. It is shown that for certain values of the control parameter, both the local behavior and the global behavior of solutions… 



Interval Methods for Rigorous Investigations of periodic orbits

  • Z. Galias
  • Mathematics, Physics
    Int. J. Bifurc. Chaos
  • 2001
In this paper, we investigate the possibility of using interval arithmetic for rigorous investigations of periodic orbits in discrete-time dynamical systems with special emphasis on chaotic systems.

Predictive Feedback Control Method for Stabilization of Continuous Time Systems

The Predictive Feedback Control method is generalized by extending it to stabilize continuous time systems to solve the system using Euler method for its simplicity and then the PFC method is applied to the discretized system.

Average predictive control for nonlinear discrete dynamical systems.

This work proposes the generalization of predictive control method for resolving the stabilization problem of unstable periodic orbits in discrete nonlinear dynamical systems and embodies the development of control method proposed by B.T. Polyak.

Rigorous investigations of Ikeda map by means of interval arithmetic

Various tools for studying dynamical systems implemented in interval arithmetic are presented, including an algorithm for finding all low-period cycles enclosed in a specified region, and proving the existence of symbolic dynamics of a given type embedded in the map.

Stabilizing Chaos with Predictive Control

A novel approach to controlling chaos in discrete-time nonlinear autonomous systems is proposed. A desired unstable periodic orbit is stabilized by small control using the predicted trajectory of the

Can we trust in numerical computations of chaotic solutions of dynamical systems

A survey of the topic based on new structures like hyperbolic and/or strange attractors, only few, but well studied models is presented.

Iteration of endomorphisms on the real axis and representation of numbers

We study a class of endomorphisms of the set of real numbers x of the form: ~ 2014~ ~/M, ~ E [0, 2]. The function f is continuous, convex with a single maximum but otherwise arbitrary; A is a real