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Collective behavior is studied in globally coupled maps. Several coherent motions exist, even in fully desynchronized state. To characterize the collective behavior, we introduce scaling transformation of parameter, and detect the…
The amplitude of fluctuation-induced patterns might be expected to be proportional to the strength of the driving noise, suggesting that such patterns would be difficult to observe in nature. Here, we show that a large class of…
We consider a two-node fluid network with batch arrivals of random size having a heavy-tailed distribution. We are interested in the tail asymptotics for the stationary distribution of a two-dimensional queue-length process. The tail…
A new, extended nonlinear framework of the ordinary real analysis incorporating a novel concept of {\em duality structure} and its applications into various nonlinear dynamical problems is presented. The duality structure is an asymptotic…
The Fluctuation Theorem gives an analytical expression for the probability of observing second law violating dynamical fluctuations, in nonequilibrium systems. At equilibrium statistical mechanical fluctuations are known to be ensemble…
The auto-correlation function and the frequency power spectral density due to a super-position of uncorrelated exponential pulses are considered. These are shown to be independent of the degree of pulse overlap and thereby the intermittency…
We study the role of noise on the nature of the transition to collective motion in dry active matter. Starting from field theories that predict a continuous transition at the deterministic level, we show that fluctuations induce a…
The effect of external fluctuations on the formation of spatial patterns is analysed by means of a stochastic Swift-Hohenberg model with multiplicative space-correlated noise. Numerical simulations in two dimensions show a shift of the…
The peculiar characteristics of random laser emission have been studied in many different media, leading to a classification of the working regimes based on the statistics of spectral fluctuations. Alongside such studies, the possibility to…
A generic saddle-node bifurcation is proposed to modelize fast transitions of finite amplitude arising in geophysical (and perhaps other) contexts, when they result from the intrinsic dynamics of the system. The fast transition is…
In this paper, we study the fluctuations of sums of random variables with distribution defined as a mixture of light-tail and truncated heavy-tail distributions. We focus on the case when both the mixing coefficient and the truncation level…
The energy of an elastic manifold in a random landscape at T=0 is shown numerically to obey a probability distribution that depends on size of the box it is put into. If the extent of the spatial fluctuations of the manifold is much less…
In this paper, we derive higher-order expansions of $L$-statistics of independent risks $X_1, \ldots, X_n$ under conditions on the underlying distribution function $F$. The new results are applied to derive the asymptotic expansions of…
Random multiplicative growth with redistribution generates stationary Pareto wealth tails in the Bouchaud-M\'ezard model, but assumes a fixed multiplicative noise intensity. This is restrictive for physical and financial growth processes,…
A light beam normally incident upon an uniformly moving dielectric medium is in general subject to bendings due to a transverse Fresnel-Fizeau light drag effect. In conventional dielectrics, the magnitude of this bending effect is very…
Dynamics of double membrane films is investigated in the long-wavelength limit including the overdamped squeezing mode. We demonstrate that thermal fluctuations essentially modify the character of the mode due to its nonlinear coupling to…
We study 2D fronts propagating up a co-moving reaction rate gradient in finite number reaction-diffusion systems. We show that in a 2D rectangular channel, planar solutions to the deterministic mean-field equation are stable with respect to…
Transient responses in disordered systems typically show a heavy-tail relaxation behavior: the decay time constant increases as time increases, revealing a spectral distribution of time constants. The asymptotic value of such transients is…
Mobility edge transitions from localized to extended states have been observed in two and three dimensional systems, for which sound theoretical explanations have also been derived. One-dimensional lattice models have failed to predict…
A two-dimensional lattice model for the formation and evolution of shear bands in granular media is proposed. Each lattice site is assigned a random variable which reflects the local density. At every time step, the strain is localized…