Related papers: Extension of Lorenz Unpredictability
We comment on mathematical results about the statistical behavior of Lorenz equations an its attractor, and more generally to the class of singular hyperbolic systems. The mathematical theory of such kind of systems turned out to be…
In recent years, the topic of car-following has experimented an increased importance in traffic engineering and safety research. This has become a very interesting topic because of the development of driverless cars…
The periodic motion of a classical point particle in a one-dimensional double-well potential acquires a surprising degree of complexity if friction is added. Finite uncertainty in the initial state can make it impossible to predict in which…
The predictability of weather and climate is strongly state-dependent: special and extremely relevant atmospheric states like blockings are associated with anomalous instability. Indeed, typically, the instability of a chaotic dynamical…
The tremendous popular success of Chaos Theory shares some common points with the not less fortunate Relativity: they both rely on a misunderstanding. Indeed, ironically , the scientific meaning of these terms for mathematicians and…
We study an influence of nonlinear dissipation and external perturbations onto transition scenarious to chaos in Lorenz-Haken system. It will be show that varying in external potential parameters values leads to parameters domain formation…
Due to their relevance to geophysical systems, the investigation of multiscale systems through the lens of statistical mechanics has gained popularity in recent years. The aim of our work is the characterization of the nonequilibrium…
We examine synchronization of identical chaotic systems coupled in a drive/response manner. A rigorous criterion is presented which, if satisfied, guarantees that synchronization to the driving trajectory is linearly stable to…
The influence of noise on the generalized synchronization regime in the chaotic systems with dissipative coupling is considered. If attractors of the drive and response systems have an infinitely large basin of attraction, generalized…
Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion…
This article briefly introduces the generalized Lorenz systems family, which includes the classical Lorenz system and the relatively new Chen system as special cases, with infinitely many related but not topologically equivalent chaotic…
We study and characterize a direct route to high-dimensional chaos (i.e. not implying an intermediate low-dimensional attractor) of a system composed out of three coupled Lorenz oscillators. A geometric analysis of this medium-dimensional…
A chaotic system under periodic forcing can develop a periodically visited strange attractor. We discuss simple models in which the phenomenon, quite easy to see in numerical simulations, can be completely studied analytically.
The realization of novel scenario involving transitions between different types of chaotic attractors is investigated for the Rossler system. Characteristic features indicative of the presence of generalized intermittency scenario in this…
Contrary to the established view of the Lorenz system as an archetype of dissipative chaos lacking conserved quantities, this work rigorously demonstrates the existence of a novel class of history-dependent dynamical invariants. Through a…
In chaotic dynamical systems, an infinitesimal perturbation is exponentially amplified at a time-rate given by the inverse of the maximum Lyapunov exponent $\lambda$. In fully developed turbulence, $\lambda$ grows as a power of the Reynolds…
We describe some recent results on the dynamics of singular-hyperbolic (or Lorenz-like) attractors: attractors in this class are expansive and so sensitive with respect to initial data; they admit a unique physical measure whose support is…
This letter suggests a new way to investigate 3-D chaos in spatial and frequency domains simultaneously. After spatially decomposing the Lorenz attractor into two separate scrolls with peaked spectra and a 1-D discrete-time zero-crossing…
Generalized chaotic synchronization regime is observed in the unidirectionally coupled one-dimensional Ginzburg-Landau equations. The mechanism resulting in the generalized synchronization regime arising in the coupled spatially extended…
Lorenz attractors are important objects in the modern theory of chaos. The reason from one side is that they are met in various natural applications (fluid dynamics, mechanics, laser dynamics, etc.). At the same time, Lorenz attractors are…