Related papers: Chaos indicators for non-linear dynamics in circul…
In Hermitian systems, Krylov complexity has emerged as a powerful diagnostic of quantum dynamics, capable of distinguishing chaotic from integrable phases, in agreement with established probes such as spectral statistics and…
Circular particle accelerators at the energy frontier are based on superconducting magnets that are extremely sensitive to beam losses as these might induce quenches, i.e.\ transitions to the normal-conducting state. Furthermore, the energy…
We have developed the {\it general method} for the description of {\it separatrix chaos}, basing on the analysis of the separatrix map dynamics. Matching it with the resonant Hamiltonian analysis, we show that, for a given amplitude of…
Synchronized chaos has previously been predicted and observed in a small number (3) of mutually coupled lasers. In this work, we demonstrate that this phenomenon can theoretically persist in significantly broader scenarios, extending to…
Identifying the types of orbits is an important topic in the study of chaotic dynamical systems. Beyond the well-known distinctly chaotic and regular motions, we focus on dynamics occurring in regions where regular and chaotic motions…
We provide appropriate tools for the analysis of dynamics and chaos for one-dimensional systems with periodic boundary conditions. Our approach allows for the investigation of the dependence of the largest Lyapunov exponent on various…
Searching recurrent patterns in complex systems with high-dimensional phase spaces is an important task in diverse fields. In the current work, an improved scheme is proposed to accelerate the recently designed variational approach for…
We consider the number of Bowen sets which are necessary to cover a large measure subset of the phase space. This introduce some complexity indicator characterizing different kind of (weakly) chaotic dynamics. Since in many systems its…
We find a novel characteristic for chaotic motion by introducing Shannon entropy for periodic orbits, quasiperiodic orbits, and chaotic orbits.We compare our approach with the previous methods including Poincar\'{e} Section, Lyapunov…
The Smaller Alignment Index (SALI) is a very useful and efficient indicator that can distinguish rapidly and with certainty between ordered and chaotic motion in Hamiltonian systems. This is based on the different behavior of the SALI in…
In the present article, we introduce and also deploy a new, simple, very fast and efficient method, the Fast Norm Vector Indicator (FNVI) in order to distinguish rapidly and with certainty between ordered and chaotic motion in Hamiltonian…
Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…
In this paper we introduce some weak dynamical properties by using subbases for the phase space. Among them, the notion of light chaos is the most significant. Severalexamples, which clarify the relationships between this kind of chaos and…
The dynamics of chaotic systems are, by definition, exponentially sensitive to initial conditions and may appear rather random. In this work, we explore relations between the chaotic dynamics of an observable and the dynamics of information…
We study chaos dynamics of spinning particles in Kerr spacetime of rotating black holes use the Papapetrou equations by numerical integration. Because of spin, this system exists many chaos solutions, and exhibits some exceptional dynamic…
We predict that continuously monitored quantum dynamics can be chaotic. The optimal paths between past and future boundary conditions can diverge exponentially in time when there is time-dependent evolution and continuous weak monitoring.…
Nonlinear networks with time-delayed couplings may show strong and weak chaos, depending on the scaling of their Lyapunov exponent with the delay time. We study strong and weak chaos for semiconductor lasers, either with time-delayed…
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…
We study the regular or chaotic nature of orbits in a 3D potential describing a triaxial galaxy surrounded by a spherical dark halo component. Our numerical calculations show, that the percentage of chaotic orbits decreases exponentially,…
The scaling behavior of the maximal Lyapunov exponent in chaotic systems with time-delayed feedback is investigated. For large delay times it has been shown that the delay-dependence of the exponent allows a distinction between strong and…