Related papers: Extensive Chaos in the Lorenz-96 Model
Fractal scaling--a power-law behavior of the number of boxes needed to tile a given network with respect to the lateral size of the box--is studied. We introduce a new box-covering algorithm that is a modified version of the original…
In this article, we propose an anomalous chaotic system of the scaling-law ordinary differential equations involving the Mandelbrot scaling law. This chaotic behavior shows the "Wukong" effect. The comparison among the Lorenz and…
The study of dynamics in general relativity has been hampered by a lack of coordinate independent measures of chaos. Here I review a variety of invariant measures for quantifying chaotic dynamics in relativity that exploit the coordinate…
Atmospheric flows exhibit selfsimilar fractal spacetime fluctuations manifested as the fractal geometry to global cloud cover pattern and inverse power law form for power spectra of meteorological parameters such as windspeed, temperature,…
A quantum analysis of the vacuum Bianchi IX model is performed, focusing in particular on the chaotic nature of the system. The framework constructed here is general enough for the results to apply in the context of any theory of quantum…
Chaotic bursting behaviors have been observed by many authors in neural dynamics mainly in the transition between different kinds of bursting behavior. As a well-known three-dimensional ODEs model with various bursting solutions, the…
Motivated by recent progress in data assimilation, we develop an algorithm to dynamically learn the parameters of a chaotic system from partial observations. Under reasonable assumptions, we rigorously establish the convergence of this…
A variant of the complex Ginzburg-Landau equation is used to investigate the frequency locking phenomena in spatially extended systems. With appropriate parameter values, a variety of frequency-locked patterns including flats, $\pi$ fronts,…
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…
Large deviations in chaotic dynamics have potentially significant and dramatic consequences. We study large deviations of series of finite lengths $N$ generated by chaotic maps. The distributions generally display an exponential decay with…
A type of chaos called laminar chaos was found in singularly perturbed dynamical systems with periodically [Phys. Rev. Lett. 120, 084102 (2018)] and quasiperiodically [Phys. Rev. E 107, 014205 (2023)] time-varying delay. Compared to…
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…
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…
Chaotic motion in time of a number of macroscopic systems has been analyzed, in the framework of scale relativity, as motion in a fractal space with topological dimension 3 and geodesics with fractal dimension 2. The motion equation is then…
Studies of dynamical stability (chaotic versus regular motion) in galactic dynamics often rely on static analytical models of the total gravitational potential. Potentials based upon self-consistent N-body simulations offer more realistic…
The spacing intervals of adjacent Riemann zeta zeros(non-trivial) exhibit fractal(irregular) fluctuations generic to dynamical systems in nature such as fluid flows, heart beat patterns, stock market price index, etc., and are associated…
While extensive research has been conducted on chaos emerging from a dynamical system's temporal dynamics, our research examines extreme sensitivity to initial conditions in discrete-time dynamical systems from a geometrical perspective.…
The understanding of the fundamental properties of the climate system has long benefitted from the use of simple numerical models able to parsimoniously represent the essential ingredients of its processes. Here we introduce a new model for…
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…
It is a fundamental problem how the universal concept of classical chaos emerges from the microscopic description of quantum mechanics. We here study standard classical chaos in a framework of quantum mechanics. In particular, we design a…