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Many systems in nature, from ferromagnets to flocks of birds, exhibit ordering phenomena on the large scale. In physical systems order is statistically robust for large enough dimensions, with relative fluctuations due to noise vanishing…
The statistical behavior of a nonlinear system described by a mapping with phase rotation is studied. We use the Kolmogorov-Chapman equations for the multi-time probability distribution functions for investigation of dynamics under the…
Quantum non-Markovianity modifies the environmental decoherence of a system. This situation is enriched in complex systems owing to interactions among subsystems. We consider the problem of distinguishing the multiple sources of…
This work considers state dynamics driven by Periodic Autoregressive Moving Average noise, and control of the system over time. Such processes appear frequently in applications involving the environment, such as energy and agriculture.…
We introduce and study a stochastic model for the dynamics of colonial species, which reproduce through fission or fragmentation. The fission rate depends on the relative sizes of colonies in the population, and the growth rate of colonies…
The literature is rich with studies, analyses, and examples on parameter estimation for describing the evolution of chaotic dynamical systems based on measurements, even when only partial information is available through observations.…
In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the Mori-Zwanzig formalism. The Mori-Zwanzig equations…
According to empirical observations, some pattern formation phenomena in driven many-particle systems are more pronounced in the presence of a certain noise level. We investigate this phenomenon of fluctuation-driven ordering with a…
We study a control system resembling a singularly perturbed system whose variables are decomposed into groups that change their values with rates of different orders of magnitude. We establish that the slow trajectories of this system are…
Previously, we developed a population model incorporating the Allee effect and periodic environmental fluctuations, in which organisms alternate between nomadic and colonial behaviours. This switching strategy is regulated by biological…
We provide quantitative estimates in total variation distance for positive semi-groups, which can be non-conservative and non-homogeneous. The techniques relies on a family of conservative semigroups that describes a typical particle and…
This paper deals with the analysis of stochastic systems which can be described by a Langevin equation. By the method presented in this paper drift and diffusion terms of the corresponding Fokker-Planck equation can be extracted from the…
A bifurcating system subject to multiplicative noise can exhibit on-off intermittency close to the instability threshold. For a canonical system, we discuss the dependence of this intermittency on the Power Spectrum Density (PSD) of the…
This paper presents a systematic numerical study of the effects of noise on the invariant probability densities of dynamical systems with varying degrees of hyperbolicity. It is found that the rate of convergence of invariant densities in…
The effects of intrinsic noise on stochastic delay systems is studied within an expansion in the inverse system size. We show that the stochastic nature of the underlying dynamics may induce oscillatory behaviour in parameter ranges where…
We study the effects of noise on a recently discovered form of intermittency, referred to as in-out intermittency. This type of intermittency, which reduces to on-off in systems with a skew product structure, has been found in the dynamics…
Given a quantum Hamiltonian, we explain how the dynamical properties of the underlying classical system affect the behaviour of quantum eigenstates in the semi-classical limit. We study this problem via the notion of semiclassical measures.…
We investigate a general class of models for swarming/self-collective behaviour in domains with boundaries. The model is expressed as a stochastic system of interacting particles subject to both reflecting boundary condition and common…
In many applications, the common assumption that a driving noise process affecting a system is independent or Markovian may not be realistic, but the noise process may be assumed to be stationary. To study such problems, this paper…
Weak noise smooths out fractals in a chaotic state space and introduces a maximum attainable resolution to its structure. The balance of noise and deterministic stretching/contraction in each neighborhood introduces local invariants of the…