Related papers: Chaos indicators for non-linear dynamics in circul…
We study how spatiotemporal chaos in dynamical systems can be controlled by stochastically returning them to their initial conditions. Focusing on discrete nonlinear maps, we analyze how key measures of chaos -- the Lyapunov exponent and…
In this paper we apply the method of Lagrangian descriptors as an indicator to study the chaotic and regular behavior of trajectories in the phase space of the classical double pendulum system. In order to successfully quantify the degree…
Deterministic chaos is phenomenon from nonlinear dynamics and it belongs to greatest advances of twentieth-century science. Chaotic behavior appears apart of mathematical equations also in wide range in observable nature, so as in there…
Turbulence and chaos play a fundamental role in stellar convective zones through the transportof particles, energy and momentum, and in fast dynamos, through the stretching, twisting and folding of magnetic flux tubes. A particularly…
We introduce new machine-learning techniques for analyzing chaotic dynamical systems. The primary objectives of the study include the development of a new and simple method for calculating the Lyapunov exponent using only two trajectory…
Chirality refers to the property that an object and its mirror image cannot overlap each other by spatial rotation and translation, and can be found in various research fields. We here propose chiral chaos and construct a chiral chaotic…
Maximizing the rf bandwidth associated with the chaotic output from tailored operation of nonlinear semiconductor laser systems is an ongoing research effort. The early pioneering research was done in semiconductor laser with delayed…
The method of detection of the unstable periodic spatio-temporal states of spatial extended chaotic systems has been proposed. The application of this method is illustrated by the consideration of two different systems: i) the fluid model…
Nonlinear dynamics has an important role when designing modern synchrotron lattices. In this letter, we introduce a new method of using a square matrix to analyze periodic nonlinear dynamical systems [1, 2]. Applying the method to the…
Optical non-linearities, such as thermo-optic effects and free-carrier-dispersion, are often considered as undesired effects in silicon-based resonators and, more specifically, optomechanical (OM) cavities, affecting the relative detuning…
We show that the output of systems with time-varying delay can exhibit a new kind of chaotic behavior characterized by laminar phases, which are periodically interrupted by irregular bursts. Within each laminar phase the output intensity…
Chaos indicators, like the Lyapunov exponent lambda, are widely used in celestial mechanics to characterize the dynamical behavior of bodies. The stability of their orbit can be determined by the calculation of the local exponential…
We propose a novel approach which exploits chaos to enhance classification accuracy. Specifically, the available data that need to be classified are treated as vectors that are first lifted into a higher-dimensional space and then used as…
We experimentally report on the detection of chaos from a free-running commercial broad-area VCSEL without the need for external perturbation such as optical feedback, injection or current modulation. The evolution of nonlinear dynamics…
In a recent work of Wu, Wang, Sun and Liu, a second-order explicit symplectic integrator was proposed for the integrable Kerr spacetime geometry. It is still suited for simulating the nonintegrable dynamics of charged particles moving…
An algorithm for detecting unstable periodic orbits in chaotic systems [Phys. Rev. E, 60 (1999), pp. 6172-6175] which combines the set of stabilising transformations proposed by Schmelcher and Diakonos [Phys. Rev. Lett., 78 (1997), pp.…
As cities around the world aim to improve walkability and safety, understanding the irregular and unpredictable nature of pedestrian behavior has become increasingly important. This study introduces a data-driven framework for modeling…
The identification of complex periodic windows in the two-dimensional parameter space of certain dynamical systems has recently attracted considerable interest. While for discrete systems, a discrimination between periodic and chaotic…
We propose a mechanism by which the efficiency of mixing in chaotic flows can be enhanced. Our mechanism consists of introducing small changes in the system parameters in regions of phase space where the local Lyapunov exponent falls…
A new method based on the phenomenon of synchronization and the properties of chaos is proposed to reduce interference in the transferred chaotic signals of synchronized systems. In this paper, the interference is considered as a series of…