Related papers: On the timescale at which statistical stability br…
A model demonstrating existence of a thermodynamically stable quantum time-space crystal has been proposed and studied. This state is characterized by an order parameter periodic in both real and imaginary times. The average of the order…
A dynamical system that undergoes a supercritical Hopf's bifurcation is perturbed by a multiplicative Brownian motion that scales with a small parameter $\epsilon$. The random fluctuations of the system at the critical point are studied…
The paper shows sufficiency conditions for stability of continuous periodic orbits under phase uncertainty. Phase based uncertainty is a trait of bipedal walking robots, where the desired trajectories are parameterized by a monotonous…
Why are human societies unstable? Theories based on the observation of recurring patterns in historical data indicate that economic inequality, as well as social factors are key drivers. So far, models of this phenomenon are more…
Dynamical systems often contain oscillatory forces or depend on periodic potentials. Time or space periodicity is reflected in the properties of these systems through a dependence on the parameters of their periodic terms. In this paper we…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
We develop a practical approach to establish the stability, that is, the recurrence in a given set, of a large class of controlled Markov chains. These processes arise in various areas of applied science and encompass important numerical…
Unstable periodic orbits scar wave functions in chaotic systems. This also influences the associated spectra, that follow the otherwise universal Porter--Thomas intensity distribution. We show here how this deviation extend to other longer…
We consider a dynamics generated by families of maps whose invariant density depends on a parameter a and where a itself obeys a stochastic or periodic dynamics. For slowly varying a the long-term behavior of iterates is described by a…
We analyze a numerical instability that occurs in the well-known split-step Fourier method on the background of a soliton. This instability is found to be very sensitive to small changes of the parameters of both the numerical grid and the…
While there have been many studies examining the stability of hierarchical triple systems, the meaning of ``stability'' is somewhat vague and has been interpreted differently in previous literatures. The present paper focuses on ``Lagrange…
An autonomous system of ordinary differential equations in the plane with a centre-saddle bifurcation is considered. The influence of time damped perturbations with power-law asymptotics is investigated. The particular solutions tending at…
With the rise of network science old topics in ecology and economics are resurfacing. One such topic is structural stability (often referred to as qualitative stability or sign stability). A system is deemed structurally stable if the…
We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…
We present conditions on families of diffeomorphisms that guarantee statistical stability and SRB entropy continuity. They rely on the existence of horseshoe-like sets with infinitely many branches and variable return times. As an…
A review of the statistical properties of earthquakes is provided, centered mainly in the work of the author (apologies for that). We explain the scaling law for the recurrence-time distributions, its universal character for stationary…
We establish stability criterion for a two-class retrial system with Poisson inputs, general class-dependent service times and class-dependent constant retrial rates. We also characterise an interesting phenomenon of partial stability when…
When the discrete time-translation symmetry of isolated, periodically driven systems is spontaneously broken, a new phase of matter can emerge. We review some recent developments on both the theoretical underpinnings and experimental…
The motion of a satellite around a planet can be studied by the Hill model, which is a modification of the restricted three body problem pertaining to motion of a satellite around a planet. Although the dynamics of the circular Hill model…
We analyze different data of the variation of the fine structure constant obtained with different methods to check their consistency.We test consistency using the modified Student test and confidence intervals. We split the data sets in…