Related papers: Chaos: a bridge from microscopic uncertainty to ma…
Chaotic behavior in dynamical systems poses a significant challenge in trajectory control, traditionally relying on computationally intensive physical models. We present a machine learning-based algorithm to compute the minimum control…
A heuristic generalization of the Boltzmann-Gibbs microcanonical entropy is proposed, able to describe meta-equilibrium features and evolution of macroscopic systems. Despite its simple-minded derivation, such a function of "collective…
The Chirikov resonance-overlap criterion predicts the onset of global chaos if nonlinear resonances overlap in energy, which is conventionally assumed to require a non-small magnitude of perturbation. We show that, for a time-periodic…
The propagation of chaos is a central concept of kinetic theory that serves to relate the equations of Boltzmann and Vlasov to the dynamics of many-particle systems. Propagation of chaos means that molecular chaos, i.e., the stochastic…
Laboratory earthquakes exhibit characteristics of a low dimensional random attractor with a dimension similar to that of natural slow earthquakes. A model of stochastic differential equations based on rate and state-dependent friction…
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…
Chaotic synchronization is generally extremely sensitive to the presence of noise and other inference in the channel. Is this sensitivity a fundamental property of chaotic synchronization or is it related to the choice of synchronization…
We propose a stochastic sampling approach to identify stability boundaries in general dynamical systems. The global landscape of Lyapunov exponent in multi-dimensional parameter space provides transition boundaries for stable/unstable…
In shear flows like pipe flow and plane Couette flow there is an extended range of parameters where linearly stable laminar flow coexists with a transient turbulent dynamics. When increasing the amplitude of a perturbation on top of the…
In finite-dimensional, chaotic, Lorenz-like wave-particle dynamical systems one can find diffusive trajectories, which share their appearance with that of laminar chaotic diffusion [Phys. Rev. Lett. 128, 074101 (2022)] known from delay…
Phase transitions not allowed in equilibrium steady states may happen however at the fluctuating level. We observe for the first time this striking and general phenomenon measuring current fluctuations in an isolated diffusive system. While…
The fluidic pinball has been recently proposed as an attractive and effective flow configuration for exploring machine learning fluid flow control. In this contribution, we focus on the route to chaos in this system without actuation, as…
Chaos is an inherently dynamical phenomenon traditionally studied for trajectories that are either permanently erratic or transiently influenced by permanently erratic ones lying on a set of measure zero. The latter gives rise to the final…
How is the irreversibility of a high-dimensional chaotic system controlled by the heterogeneity in the non-reciprocal interactions among its elements? In this paper, we address this question using a stochastic model of random recurrent…
Transient chaos is a characteristic behavior in nonlinear dynamics where trajectories in a certain region of phase space behave chaotically for a while, before escaping to an external attractor. In some situations the escapes are highly…
Controlling entanglement and coherence is central to quantum information, yet the two resources often exhibit antagonistic trends and are difficult to optimize within a single platform. Here we show that chaos enables switchable eigenstate…
The transition to chaos in the subcritical regime of counter-rotating Taylor-Couette flow is investigated using a minimal periodic domain capable of sustaining coherent structures. Following a Feigenbaum cascade, the dynamics are found to…
A statistical analysis of the prime numbers indicates possible traces of quantum chaos. We have computed the nearest neighbor spacing distribution, number variance, skewness, and excess for sequences of the first N primes for various values…
In the sciences in general, the phrase "route to chaos" has come to refer to a metaphor when some physical, biological, economic, or social system transitions from one exhibiting order to one displaying randomness (or chaos). Sometimes the…
Evolutionary game theory has traditionally employed deterministic models to describe population dynamics. These models, due to their inherent nonlinearities, can exhibit deterministic chaos, where population fluctuations follow complex,…