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The optomechanical systems produce chaotic behaviour due to nonlinear interaction between photons and phonons, and the same systems are used to understand the synthetic fields as well. Here, we report on the study of chaotic behaviour in…
In this note we will discuss the notion of robust chaos, and show that (i) there are natural one-parameter families with robust chaos and (ii) hyperbolicity is dense within generic one-parameter families (and so these families are not…
We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a…
Chaos is a fundamental phenomenon in nonlinear dynamics, manifesting as irregular and unpredictable behavior across various physical systems. Among the diverse routes to chaos, intermittent chaos is a distinct transition pathway,…
A widely accepted definition of ``quantum chaos'' is ``the behavior of a quantum system whose \emph{classical} \emph{limit is chaotic}''. The dynamics of quantum-chaotic systems is nevertheless very different from that of their classical…
The thermodynamic formalism of Ruelle, Sinai, and Bowen, in which chaotic properties of dynamical systems are expressed in terms of a free energy-type function - called the topological pressure - is applied to a Lorentz Lattice Gas, as…
Collective behavior is studied in globally coupled maps with distributed nonlinearity. It is shown that the heterogeneity enhances regularity in the collective dynamics. Low-dimensional quasiperiodic motion is often found for the…
Synchronization, that occurs both for non-chaotic and chaotic systems, is a striking phenomenon with many practical implications in natural phenomena. However, even before synchronization, strong correlations occur in the collective…
A new type of asymptotic behavior in a game dynamics system is discovered. The system exhibits behavior which combines chaotic motion and attraction to heteroclinic cycles; the trajectory visits several unstable stationary states repeatedly…
Disordered systems are an important class of models in statistical mechanics, having the defining characteristic that the energy landscape is a fixed realization of a random field. Examples include various models of glasses and polymers.…
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…
Collective temporal organization in complex systems is commonly attributed to synchronization, resonance, or proximity to dynamical instabilities. Here we identify a distinct mechanism by which coherent, synchronization-like behavior can…
Using semiclassical methods, it is possible to construct very accurate approximations in the short wavelength limit of quantum dynamics that rely exclusively on classical dynamical input. For systems whose classical realization is strongly…
We construct a family of chaotic dynamical systems with explicit broad distributions, which always violate the central limit theorem. In particular, we show that the superposition of many statistically independent, identically distributed…
We numerically study quantum chaos properties of long-range XXZ dipolar Hamiltonian spin systems. Two geometries are considered: (i) an open chain with 19 spins, (ii) a face-centered cubic lattice with 14 spins. Energy level-spacing…
We establish the emergence of chaotic motion in optomechanical systems. Chaos appears at negative detuning for experimentally accessible values of the pump power and other system parameters. We describe the sequence of period doubling…
We review some recent work on the synchronization of coupled dynamical systems on a variety of networks. When nodes show synchronized behaviour, two interesting phenomena can be observed. First, there are some nodes of the floating type…
We examine the mutual synchronization of a one dimensional chain of chaotic identical objects in the presence of a stimulus applied to the first site. We first describe the characteristics of the local elements, and then the process whereby…
As well-known, the concept "hypercyclic" in operator theory is the same as the concept "transitive" in dynamical system. Now the class of hypercyclic operators is well studied. Following the idea of research in hypercyclic operators, we…
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…