Related papers: Aging Induced Multifractality
Many complex systems, ranging from migrating cells to animal groups, exhibit stochastic dynamics described by the underdamped Langevin equation. Inferring such an equation of motion from experimental data can provide profound insight into…
The irreversibility of the equations of classical dynamics (the Hamilton equations and the Liouville equation) in the space with multifractal time is demonstrated. The time is given on multifractal sets with fractional dimensions. The last…
We summarize studies of growing lengths in different aging systems. The article is structured as follows. We recall the definition of a number of observables, typically correlations and susceptibilities, that give access to dynamic and…
We consider a persistent random walk on an inhomogeneous environment where the reflection probability depends only on the distance from the origin. Such an environment is the result of an average over all realizations of disorder of a…
The paper presents a multidimensional model for nonlinear Markovian random walks that generalizes one we developed previously (Phys. Rev. E v.79, 011110, 2009) in order to describe the Levy type stochastic processes in terms of continuous…
Literature is full of inference techniques developed to estimate the parameters of stochastic dynamical systems driven by the well-known Brownian noise. Such diffusion models are often inappropriate models to properly describe the dynamics…
When complex systems are driven to extinction by some external factor, their non-stationary dynamics can present an intermittent behaviour between relative tranquility and burst of activity whose consequences are often catastrophic. To…
In this paper we study the problem of statistical inference for a continuous-time moving average L\'evy process of the form $$Z_{t} = \int_{\mathbb{R}}\mathcal{K}(t-s)\, dL_{s},\quad t\in\mathbb{R}$$ with a deterministic kernel (\K\) and a…
Recent evidence suggests that physiological signals under healthy conditions may have a fractal temporal structure. We investigate the possibility that time series generated by certain physiological control systems may be members of a…
Complex systems having metastable elements often demonstrate nearly log-time relaxations and a kind of aging: repeated stimuli weaken the system's relaxational response. Granular matter is known to exhibit a wealth of such behaviors, for…
Introducing a general class of one-dimensional single-file systems (meaning that particle crossings are prohibited) of interacting hardcore particles with internal degrees of freedom (called charge), we exhibit a novel type of dynamical…
Amorphous materials driven away from equilibrium display a diverse repertoire of complex, history-dependent behaviors. One striking feature is a failure to return to equilibrium after an abrupt change in otherwise static external…
A multiphasic constitutive model of the skin that implicitly accounts for the process of intrinsic (i.e.\ chronological) ageing via variation of the constitutive parameters is proposed. The structurally-motivated constitutive formulation…
The main goal of the work is to study the stochastic averaging principle for two time-scales stochastic evolution equations driven by L\'evy process. The solution of reduced equation with modified coefficient is derived to approximate the…
We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a L\'evy walk process,…
The exact equations of motion for microscopic density of classical many-body system with account of inter-particle retarded interactions are derived. It is shown that interactions retardation leads to irreversible behaviour of many-body…
We discuss diffusion properties of a dynamical system, which is characterised by long-tail distributions and finite correlations. The particle velocity has the stable L\'evy distribution; it is assumed as a jumping process (the kangaroo…
We present a general class of spatio-temporal stochastic processes describing the causal evolution of a positive-valued field in space and time. The field construction is based on independently scattered random measures of Levy type whose…
Building on an analogy with conformal invariance, local scale transformations consistent with dynamical scaling are constructed. Two types of local scale invariance are found which act as dynamical space-time symmetries of certain non-local…
Long memory processes driven by L\'evy noise with finite second-order moments have been well studied in the literature. They form a very rich class of processes presenting an autocovariance function which decays like a power function. Here,…