arXiv subjects

Abhijit Bera

Publications and source records attributed to Abhijit Bera.

3 recordsLinked to original sources

arXiv2026

Decomposition of Anomalous Diffusion in two-state random walks

Two-state stochastic models, where motion alternates between distinct dynamical modes, are widely observed in complex systems. Here we study the Two-State Random Walk (TSRW), which switches between a continuous-time random walk (CTRW) rest state and a standard L'evy walk (LW) motion state, each with power-law distributed sojourn times. Using anomalous diffusion decomposition, we show that TSRWs exhibit a generic coexistence of Joseph (correlation), Noah (heavy-tailed increments), and Moses (aging) effects. Strikingly, although classical L'evy walks alone possess only the Joseph effect, both Noah and Moses effects emerge in TSRWs solely due to stochastic switching with the CTRW phase. Our results demonstrate that coupling between dynamical states can fundamentally reshape the mechanisms driving anomalous diffusion, offering a minimal yet powerful framework for transport in heterogeneous and intermittently switching environments.

nlin.AO↗

arXiv2025

Complete Decomposition of Anomalous Diffusion in Variable Speed Generalized L\'evy Walks

Variable Speed Generalized L\'{e}vy Walks (VGLWs) are a class of spatio-temporally coupled stochastic processes that unify a broad range of previously studied models within a single parametrized framework. Their dynamics consist of discrete random steps, or flights, during which the walker's speed varies deterministically with both the elapsed time and the total duration of the flight. We investigate the anomalous diffusive behavior of VGLWs and analyze it through decomposition into the three fundamental constitutive effects that capture violations of the Central Limit Theorem (CLT): the Joseph effect, reflecting long-range increment correlations, the Noah effect, arising from heavy-tailed step-size distributions with infinite variance, and the Moses effect, associated with statistical aging and non-stationarity. Our results show that anomalous diffusion in VGLWs is typically generated by a nontrivial combination of all three effects, rather than being attributable to a single mechanism. Strikingly, we find that within the VGLW framework the Noah exponent $L$, which quantifies the strength of the Noah effect, is unbounded from above, revealing a richer and more extreme landscape of anomalous diffusion than in previously studied L\'{e}vy-walk-type models.

cond-mat.stat-mech↗

arXiv2023

Exploring Chaos and Ergodic behavior of an Inductorless Circuit driven by Stochastic Parameters

There exist extensive studies on periodic and random perturbations of various continuous maps investigating their dynamics. This paper presents a random piecewise smooth map derived from a simple inductor-less switching circuit. The bifurcation parameter is bounded and randomly selected from a stationary distribution. Due to the stochasticity inherent in either the parameter values or the state variable, the time evolution of the state variable cannot be predicted at a specific time instant. We observe that the state variable exhibits completely ergodic behavior when the minimum value of the parameter is 2.0. However, the ensemble average of the state variable converges to a fixed value. For parameter values ranging from 2.0 to 3.5, the system demonstrates nonchaotic behavior, and the absolute value of the Lyapunov exponent increases monotonically with the asymmetry (ap) of the distribution from which the bifurcation parameter values are sampled. We determine the probability density function of the random map and verify its invariance under any initial condition. The most noteworthy result is the disappearance of chaotic behavior when the lower range of the distribution is varied while maintaining a fixed upper threshold for a particular distribution, even though the nonrandom map exhibits an array of periodic and chaotic behaviors within that range.

nlin.AO↗