Related papers: Scaling of the Lyapunov exponent in type-III inter…
Lyapunov exponents describe the asymptotic behavior of the singular values of large products of random matrices. A direct computation of these exponents is however often infeasible. By establishing a link between Lyapunov exponents and an…
A `persistence exponent' $\theta$ is defined for nonequilibrium critical phenomena. It describes the probability, $p(t) \sim t^{-\theta}$, that the global order parameter has not changed sign in the time interval $t$ following a quench to…
The scaling hypothesis for the coupled chotic map lattices (CML) is formulated. Scaling properties of the CML in the regime of extensive chaos observed numerically before is justified analytically. The asymptotic Liapunov exponents spectrum…
The dynamics of the system is investigated when one part of the system initially behaves in a regular manner and the other in a chaotic one. The propagation of the chaos is considered as the motion of a region with the maximal Lyapunov…
Using large-scale parallel numerical simulations we explore spatiotemporal chaos in Rayleigh-B\'enard convection in a cylindrical domain with experimentally relevant boundary conditions. We use the variation of the spectrum of Lyapunov…
In Ising model on the simple cubic lattice, we describe the inverse temperature \beta in terms of the bare-mass M and study its critical behavior by the use of delta expansion from high temperature or large M side. In the vicinity of…
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…
Critical intermittency stands for a type of intermittent dynamics in iterated function systems, caused by an interplay of a superstable fixed point and a repelling fixed point. We consider critical intermittency for iterated function…
We study the problem of mean-square exponential incremental stabilization of nonlinear systems over uncertain communication channels. We show the ability to stabilize a system over such channels is fundamentally limited and the channel…
We consider the simple random walk on Z^d, d > 2, evolving in a potential of the form \beta V, where (V(x), x \in Z^d) are i.i.d. random variables taking values in [0,+\infty), and \beta\ > 0. When the potential is integrable, the…
Lagrangian chaos is experimentally investigated in a convective flow by means of Particle Tracking Velocimetry. The Finite Size Lyapunov Exponent analysis is applied to quantify dispersion properties at different scales. In the range of…
We study the scaling properties of critical particle systems confined by a potential. Using renormalization-group arguments, we show that their critical behavior can be cast in the form of a trap-size scaling, resembling finite-size scaling…
We study changes in the chaotic properties of a many-body system undergoing a solid-fluid phase transition. To do this, we compute the temperature dependence of the largest Lyapunov exponents $\lambda_{max}$ for both two- and…
We explore, employing the renormalization-group theory, the critical scaling behavior of the permutation symmetric three-vector model that obeys non-conserving dynamics and has a relevant anisotropic perturbation which drives the system…
An exponent $\beta$ which characterises non-equilibrium coarsening processes is calculated in a deterministic solvable model of coarsening for a 1D q-state Potts system. We study how the fraction of sites P which have never changed their…
Hyperchaos is distinguished from chaos by the presence of at least two positive Lyapunov exponents instead of just one in dynamical systems. A general scenario is presented here that shows emergence of hyperchaos with a sudden large…
We present several new easy ways of generating smooth one-dimensional maps displaying robust chaos, i.e., chaos for whole intervals of the parameter. Unlike what happens with previous methods, the Lyapunov exponent of the maps constructed…
We suggest a new indicator of quantum chaos based on the logarithmic out-of-time-order correlator. On the one hand, this indicator correctly reproduces the average classical Lyapunov exponent in the semiclassical limit and directly links…
Transfer-matrix methods, with the help of finite-size scaling and conformal invariance concepts, are used to investigate the critical behavior of two-dimensional square-lattice Ising spin-1/2 systems with first- and second-neighbor…
We analyse the so-called Marginal Instability of linear switching systems, both in continuous and discrete time. This is a phenomenon of unboundedness of trajectories when the Lyapunov exponent is zero. We disprove two recent conjectures of…