Related papers: Lyapunov exponent in the Vicsek model
This paper deals with the problem of analytically computing the largest Lyapunov exponent for many degrees of freedom Hamiltonian systems. This aim is succesfully reached within a theoretical framework that makes use of a geometrization of…
We present an exact solution in the large-$N$ limit of the L\'{e}vy Sachdev-Ye-Kitaev (LSYK) model introduced in Ref. [1], wherein the couplings are drawn from a L\'{e}vy Stable distribution parameterized by a tail exponent $\mu \in [0,…
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…
The Vicsek model is a very popular individual based model which describes collective behavior among animal societies. A macroscopic version of the Vicsek model has been derived from a large scale limit of this individual based model…
We numerically investigated the quantum-classical transition in rf-SQUID systems coupled to a dissipative environment. It is found that chaos emerges and the degree of chaos, the maximal Lyapunov exponent $\lambda_{m}$, exhibits…
We consider the overdamped dynamics of a paradigmatic long-range system of particles residing on the sites of a one-dimensional lattice, in the presence of thermal noise. The internal degree of freedom of each particle is a periodic…
Collective biological systems display power laws for macroscopic quantities and are fertile probing grounds for statistical physics. Besides power laws, natural insect swarms present strong scale-free correlations, suggesting closeness to…
Dynamical billiards are paradigmatic examples of chaotic Hamiltonian dynamical systems with widespread applications in physics. We study how well their Lyapunov exponent, characterizing the chaotic dynamics, and its dependence on external…
We analyze the top Lyapunov exponent of the product of sequences of two by two matrices that appears in the analysis of several statistical mechanics models with disorder: for example these matrices are the transfer matrices for the nearest…
The out-of-time order correlator (OTOC) has been widely studied in closed quantum systems. However, there are very few studies for open systems and they are mainly focused on isolating the effects of scrambling from those of decoherence.…
We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…
In this paper, we present a framework for Stability Analysis of Systems of Coupled Linear Partial-Differential Equations. The class of PDE systems considered in this paper includes parabolic, elliptic and hyperbolic systems with Dirichelet,…
We investigate collective behavior in a $Q$-species Vicsek model with a nonreciprocal velocity alignment interaction. This system is characterized by a constant phase shift $\alpha$ in the inter-species velocity alignment rule. While the…
Lagrangian chaos is experimentally investigated in a convective flow by means of Particle Tracking Velocimetry. The Fnite Size Lyapunov Exponent analysis is applied to quantify dispersion properties at different scales. In the range of…
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…
The Lyapunov exponent for collective motion is defined in order to characterize chaotic properties of collective motion for large populations of chaotic elements. Numerical computations for this quantity suggest that such collective motion…
Various kinematical quantities associated with the statistical properties of dynamical systems are examined: statistics of the motion, dynamical bases and Lyapunov exponents. Markov partitons for chaotic systems, without any attempt at…
For a better understanding of the chaotic behavior of systems of many moving particles it is useful to look at other systems with many degrees of freedom. An interesting example is the high-dimensional Lorentz gas, which, just like a system…
Information transfer is an essential factor in determining the robustness of collective behaviour in biological systems with distributed control. The most direct way to study the information transfer mechanisms is to experimentally detect…
Eccentric mixing is a typical chaotic mixing method, and the study of its mixing characteristics is beneficial to the optimization of the mixing process. In this study, the effects of eccentricity (E/R) and rotational speed (N) on the…