Related papers: Unifying Dynamical and Structural Stability of Equ…
In this paper, we claim the availability of deterministic noises for stabilization of the origins of dynamical systems, provided that the noises have unbounded variations. To achieve the result, we first consider the system representations…
Stochastic feedback systems give rise to a variety of notions of stability. The conditions for the stability of the median, mean, and variance stability conditions differ. These conditions can be stated explicitly for scalar discrete-time…
Equilibrium topological phases are robust against weak static disorder but may break down in the strong disorder regime. Here we explore the stability of the quench-induced emergent dynamical topology in the presence of dynamical noise. We…
We examine the equilibrium and stability of an elastocapillary system to model drying-induced structural failures. The model comprises a circular elastic membrane with a hole at the center that is deformed by the capillary pressure of…
This paper studies the finite-time stability and stabilization of linear discrete time-varying stochastic systems with multiplicative noise. Firstly, necessary and sufficient conditions for finite-time stability are presented via state…
We study the entanglement evolution of two coupled qubits in interaction with an external environment and in the presence of an external magnetic field with a stochastic component. The results show the expected degradation of entanglement…
We study the synchronization of fully-connected and totally excitatory integrate and fire neural networks in presence of Gaussian white noises. Using a large deviation principle, we prove the stability of the synchronized state under…
We study an excitable active rotator with slowly adapting nonlinear feedback and noise. Depending on the adaptation and the noise level, this system may display noise-induced spiking, noise-perturbed oscillations, or stochastic busting. We…
Real world systems comprised of coupled oscillators have the ability to exhibit spontaneous synchronization and other complex behaviors. The interplay between the underlying network topology and the emergent dynamics remains a rich area of…
Analogs are nearest neighbors of the state of a system. By using analogs and their successors in time, one is able to produce empirical forecasts. Several analog forecasting methods have been used in atmospheric applications and tested on…
We analyse the effect of intrinsic fluctuations on the properties of bistable stochastic systems with time scale separation operating under1 quasi-steady state conditions. We first formulate a stochastic generalisation of the quasi-steady…
We study the dynamics of a quantum system having Hilbert space of finite dimension $d_{\mathrm{H}}$. Instabilities are possible provided that the master equation governing the system's dynamics contain nonlinear terms. Here we consider the…
Biological systems (among others) may respond to a large variety of distinct external stimuli, or signals. These perturbations will generally be presented to the system not singly, but in various combinations, so that a proper understanding…
Chaotic multiscale dynamical systems are common in many areas of science, one of the examples being the interaction of the low-frequency dynamics in the atmosphere with the fast turbulent weather dynamics. One of the key questions about…
We here describe the possibility of a synthetic description of the onset of Chaos in many degrees of freedom dynamical systems within the framework of the geometric description of dynamics. We show how this approach to instability helps to…
We study a stochastically driven, damped nonlinear oscillator whose frequency is modulated by a white or coloured noise. Using diagrammatic perturbation theory, we find that in the absence of nonlinearity, parametric modulation by a…
Regulatory dynamics in biology is often described by continuous rate equations for continuously varying chemical concentrations. Binary discretization of state space and time leads to Boolean dynamics. In the latter, the dynamics has been…
The relation between network structure and dynamics is determinant for the behavior of complex systems in numerous domains. An important long-standing problem concerns the properties of the networks that optimize the dynamics with respect…
We derive an inequality relating the finite-frequency linear response and fluctuations of an observable in a physical system. The relation holds for arbitrary observables and perturbations in general Markovian dynamics, including over- and…
We have analyzed the phenomenon of stochastic resonance in a system driven by non Gaussian noises. We have considered both white and colored noises. In the latter case we have obtained a consistent Markovian approximation that enables us to…