Related papers: Further finding results for cycles by semilinear c…
In the paper below we consider a problem of stabilization of a priori unknown unstable periodic orbits in non-linear autonomous discrete dynamical systems. We suggest a generalization of a non-linear DFC scheme to improve the rate of…
In this note, we propose a novel approach for a class of autonomous dynamical systems that allows, given some observations of the solutions, to identify its parameters and reconstruct the state vector. This approach relies on proving the…
The problem of stabilization of unstable periodic orbits of discrete nonlinear systems is considered in the article. A new generalization of the delayed feedback, which solves the stabilization problem, is proposed. The feedback is…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
We construct a family of polynomials with real coefficients that contains as a particular case the Fej\'er and Suffridge polynomials. These polynomials allow us to suggest a robust algorithm to search for cycles of arbitrary length in…
We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…
A method of stabilizing 2-cycles in discrete dynamic systems by Delayed Feedback Control is developed by using classic Harmonic Analysis.
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
In this article we consider the possibility of controlling the dynamics of nonlinear discrete systems. A new method of control is by mixing states of the system (or the functions of these states) calculated on previous steps. This approach…
We present several methods for predicting the dynamics of Hamiltonian systems from discrete observations of their vector field. Each method is either informed or uninformed of the Hamiltonian property. We empirically and comparatively…
We present a minimal control-based continuation algorithm designed to track branches of limit cycles in autonomous systems. The controller can be viewed as three sub-controllers: (i) a derivative feedback controller that is used to…
In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations…
This paper defines and develops cycle indices for the finite classical groups. These tools are then applied to study properties of a random matrix chosen uniformly from one of these groups. Properties studied by this technique will include…
In this paper, we present a control problem related to a semilinear differential equation with a moving singularity, i.e., the singular point depends on a parameter. The particularity of the controllability condition resides in the fact…
We discuss the method of folding for discrete planar systems and use it to establish the existence or non-existence of cycles or chaos in planar systems of rational difference equations with variable coefficients. These include some systems…
Controlling rhythmic systems, typically modeled as limit-cycle oscillators, is an important subject in real-world problems. Phase reduction theory, which simplifies the multidimensional oscillator state under weak input to a single phase…
We explore the problem of stabilization of unstable periodic orbits in discrete nonlinear dynamical systems. This work proposes the generalization of predictive control method for resolving the stabilization problem. Our method embodies the…
We survey the state of the art on the algorithmic analysis of discrete linear dynamical systems, focussing in particular on reachability, model-checking, and invariant-generation questions, both unconditionally as well as relative to…
A technique is introduced which allows to generate -- starting from any solvable discrete-time dynamical system involving N time-dependent variables -- new, generally nonlinear, generations of discrete-time dynamical systems, also involving…
In this paper we study the cyclicity of sliding cycles for regularized piecewise smooth visible-invisible two-folds, in the presence of singularities of the Filippov sliding vector field located away from two-folds. We obtain a slow-fast…