Related papers: Perturbing Chaos with Cycle Expansions
We present quantum graphs with remarkably regular spectral characteristics. We call them {\it regular quantum graphs}. Although regular quantum graphs are strongly chaotic in the classical limit, their quantum spectra are explicitly…
We uncover a dynamical entanglement transition in a monitored quantum system that is heralded by a local order parameter. Classically, chaotic systems can be stochastically controlled onto unstable periodic orbits and exhibit controlled and…
A new phenomenon, entrainment of chaos, which is understood as a seizure of an irregular behavior by limit cycles, is discussed. As a result, chaotic cycles appear if the chaos amplitude is small. Otherwise, the chaos is not necessarily…
In the bi-dimensional parameter space of driven oscillators, shrimp-shaped periodic windows are immersed in chaotic regions. For two of these oscillators, namely, Duffing and Josephson junction, we show that a weak harmonic perturbation…
Predictability horizon properties of chaotic dynamical systems can be related to their spectral properties. It is shown, using this relationship, that the spectral properties of the leading large-scale climate daily indices indicate a…
Fractal basin boundaries provide an important means of characterizing chaotic systems. We apply these ideas to general relativity, where other properties such as Lyapunov exponents are difficult to define in an observer independent manner.…
Polynomial chaos expansion (PCE) is a classical and widely used surrogate modeling technique in physical simulation and uncertainty quantification. By taking a linear combination of a set of basis polynomials - orthonormal with respect to…
The method of restricted path integrals allows one to effectively consider continuous (prolonged in time) measurements of quantum systems. Monitoring of the system coordinates is such a continuous measurement that allows one to describe a…
As a contribution to the inverse scattering problem for classical chaotic systems, we show that one can select sequences of intervals of continuity, each of which yields the information about period, eigenvalue and symmetry of one unstable…
Unitary transformations are an essential tool for the theoretical understanding of many systems by mapping them to simpler effective models. A systematically controlled variant to perform such a mapping is a perturbative continuous unitary…
We propose a novel approach to generate chaotic business cycles in a deterministic setting. Rather than producing chaos endogenously, we consider aggregate economic models with limit cycles and equilibriums, subject them to chaotic…
The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the…
Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic…
In this paper, we study the possible bifurcations of periodic orbits by reducing them to graphs. The aforementioned allows to study the genericity of routes to chaos, as well as to analyze their possible complexity. In particular, our…
The idea that chaos could be a useful tool for analyze nonlinear systems considered in this paper and for the first time the two time scale property of singularly perturbed systems is analyzed on chaotic attractor. The general idea…
This study redefines the analysis of Devaney chaos in multiple mappings from a set-valued perspective and introduces new conditions to characterize their chaotic behavior. As an innovative advancement, we develop computational algorithms to…
The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with…
Nonlinear dynamical systems, ranging from insect populations to lasers and chemical reactions, might exhibit sensitivity to small perturbations in their control parameters, resulting in uncertainties on the predictability of tunning…
Presence of recurrent and statistically significant unstable periodic orbits (UPOs) in time series obtained from biological systems are now routinely used as evidence for low dimensional chaos . Extracting accurate dynamical information…
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…