Related papers: How Can We Observe and Describe Chaos?
Stable chaos is a generalization of the chaotic behaviour exhibited by cellular automata to continuous-variable systems and it owes its name to an underlying irregular and yet linearly stable dynamics. In this review we discuss analogies…
This chapter offers a principled approach to the prediction of chaotic systems from data. First, we introduce some concepts from dynamical systems' theory and chaos theory. Second, we introduce machine learning approaches for…
The dynamics of a nonequilibrium system can become complex because the system has many components (e.g., a human brain), because the system is strongly driven from equilibrium (e.g., large Reynolds-number flows), or because the system…
We review some historical highlights leading to the modern perspective on the concept of chaos from the point of view of the kinetic theory. We focus in particular on the role played by the propagation of chaos in the mathematical…
While classical chaos is defined via a system's sensitive dependence on its initial conditions (SDIC), this notion does not directly extend to quantum systems. Instead, recent works have established defining both quantum and classical chaos…
Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded…
Deterministic chaos permits a precise notion of a "perfect measurement" as one that, when obtained repeatedly, captures all of the information created by the system's evolution with minimal redundancy. Finding an optimal measurement is…
We do not attempt to provide yet another definition of selforganization, but explore the conditions under which we can model a system as self-organizing. These involve the dynamics of entropy, and the purpose, aspects, and description level…
Chaotic dynamics is always characterized by swarms of unstable trajectories, unpredictable individually, and thus generally studied statistically. It is often the case that such phase-space densities relax exponentially fast to a limiting…
The presence of a period-doubling cascade in dynamical systems that depend on a parameter is one of the basic routes to chaos. It is rarely mentioned that there are virtually always infinitely many cascades whenever there is one. We report…
Many complex phenomena, from weather systems to heartbeat rhythm patterns, are effectively modeled as low-dimensional dynamical systems. Such systems may behave chaotically under certain conditions, and so the ability to detect chaos based…
In previous study [1], we proposed a new physical law applicable to both particle and thermodynamical systems. Additionally, we introduced a physical definition of chaos and self-organization. In the present work, we extend this novel…
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…
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…
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…
General relativity exhibits a unique feature not represented in standard examples of chaotic systems; it is a spacetime diffeomorphism invariant theory. Thus many characterizations of chaos do not work. It is therefore necessary to develop…
Recent progress toward classifying low-dimensional chaos measured from time series data is described. This classification theory assigns a template to the time series once the time series is embedded in three dimensions. The template…
A new type of chaos called laminar chaos was found in singularly perturbed dynamical systems with periodic time-varying delay [Phys. Rev. Lett. 120, 084102 (2018)]. It is characterized by nearly constant laminar phases, which are…
We introduce the notion of domain-structured chaos and apply it to establish a connection between stochastic dynamics and deterministic chaos.
A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…