Related papers: Rule 30: Solving the Chaos
This paper is devoted to the analysis of periodic solutions of nonlinear control-affine systems with bang-bang controls. Such problems naturally arise in periodic optimal control with constrained inputs, which have, in particular, important…
We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth random potential, which allows us to apply the ballistic $\sigma$-model approach. We analyze conditions of…
In the stochastic cellular automaton of rule 18 defined by S. Wolfram [Rev.\ Mod.\ Phys.\ {\bf 55}, 601 (1983)] the crossover of the critical behaviour induced by nonlocal site exchange was investigated using the coherent anomaly method.…
This paper is concerned with the well-posedness and regularity of the distributional solutions for the stochastic acoustic and elastic scattering problems. We show that the regularity of the solutions depends on the regularity of both the…
The paper studies digital redesign of linear time-invariant analog controllers under intermittent sampling. The sampling pattern is only assumed to be uniformly bounded, but otherwise irregular and unknown a priori. The contribution of the…
We study two-player \emph{take-away} games whose outcomes emulate two-state one-dimensional cellular automata, such as Wolfram's rules 60 and 110. Given an initial string consisting of a central data pattern and periodic left and right…
Since the appearance of H. Robbins article (1948), the central limit theorems for random sums have been studied for about 70 years. The central limit theorems for random sums of independent random variables play a very important role in…
In this article, we present a new approach to averaging in non-Hamiltonian systems with periodic forcing. The results here do not depend on the existence of a small parameter. In fact, we show that our averaging method fits into an…
Previous study of cellular automata and random Boolean networks has shown emergent behavior occurring at the edge of chaos where the randomness (disorder) of internal connections is set to an intermediate critical value. The value at which…
We investigate how the transition from integrability to nonintegrability occurs by changing the parameters of the Hamiltonian of a Heisenberg spin-1/2 chain with defects. Randomly distributed defects may lead to quantum chaos. A similar…
In this paper, the existence of subharmonic solutions for a class of non-autonomous first-order Hamiltonian systems is investigated. We also study the minimality of periods for such solutions. Our results which extend and improve many…
A central problem of linear algebra is solving linear systems. Regarding linear systems as equations over general semirings (V,otimes,oplus,0,1) instead of rings or fields makes traditional approaches impossible. Earlier work shows that the…
We consider stable periodic helixes as a generalization of stable periodic orbits. We see that in the studied class of iterated functions Chaos always arise suddenly. Therefore, we shall study the route from chaos to order rather than the…
Given a full column rank matrix $A \in \mathbb{R}^{m\times n}$ ($m\geq n$), we consider a special class of linear systems of the form $A^\top Ax=A^\top b+c$ with $x, c \in \mathbb{R}^{n}$ and $b \in \mathbb{R}^{m}$. The occurrence of $c$ in…
In this note, we study the existence and uniqueness of a positive solution to a doubly singular fractional problem with nonregular data. Besides, for some cases, we will show the existence and uniqueness of another notion of a solution,…
The resolution of linear system with positive integer variables is a basic yet difficult computational problem with many applications. We consider sparse uncorrelated random systems parametrised by the density $c$ and the ratio $\alpha=N/M$…
This work is devoted to the study of the existence and periodicity of solutions of initial differential problems, paying special attention to the explicit computation of the period. These problems are also connected with some particular…
The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…
Quantum mechanics is an extremely successful theory that agrees with every experiment. However, the principle of linear superposition, a central tenet of the theory, apparently contradicts a commonplace observation: macroscopic objects are…
This paper deals with feedback control of fractional-order Chua's system. The fractional-order Chua's system with total order less than three which exhibit chaos as well as other nonlinear behavior and theory for control of chaotic systems…