Related papers: Overshoot in biological systems modeled by Markov …

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…

The dynamical status of isolated quantum systems, partly due to the linearity of the Schrodinger equation is unclear: Conventional measures fail to detect chaos in such systems. However, when quantum systems are subjected to observation --…

We comment on some recent, yet unpublished results concerning instabilities in complex systems and their applications. In particular, we briefly describe main observations during extensive computer simulations of two lattice nonequilibrium…

The possibility that evolutionary forces -- together with a few fundamental factors such as thermodynamic constraints, specific computational features enabling information processing, and ecological processes -- might constrain the logic of…

This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…

We consider a toy model of two kinetically coupled stochastic oscillators whose dynamics is described as a Markov jump process among $N$ discrete phase states. For large $N$, it maps onto the deterministic two-oscillator Kuramoto model of…

Quasistationary states are long-lived nonequilibrium states, observed in some systems with long-range interactions under deterministic Hamiltonian evolution. These intriguing non-Boltzmann states relax to equilibrium over times which…

Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active…

The non-Markovianity of open quantum system dynamics is often associated with the bidirectional interchange of information between the system and its environment, and it is thought to be a resource for various quantum information tasks. We…

Highly-diverse ecosystems exhibit a broad distribution of population sizes and species turnover, where species at high and low abundances are exchanged over time. We show that these two features generically emerge in the fluctuating phase…

Symmetries are widespread in physical, technological, biological, and social systems and networks, including power grids. The swing equation is a classic model for the dynamics of powergrid networks. The main goal of this paper is to…

Bayesian theories of biological and brain function speculate that Markov blankets (a conditional independence separating a system from external states) play a key role for facilitating inference-like behaviour in living systems. Although it…

We present a class of stochastic processes in which the large deviation functions of time-integrated observables exhibit singularities that relate to dynamical phase transitions of trajectories. These illustrative examples include Brownian…

Nonlinear and non-stationary processes are prevalent in various natural and physical phenomena, where system dynamics can change qualitatively due to bifurcation phenomena. Traditional machine learning methods have advanced our ability to…

Non-equilibrium steady states are subject to intense investigations but still poorly understood. For instance, the derivation of Fourier law in Hamiltonian systems is a problem that still poses several obstacles. In order to investigate…

We study the dynamical properties of the ordered phases obtained in a coupled nonequilibrium system describing advection of two species of particles by a stochastically evolving landscape. The local dynamics of the landscape also gets…

Oscillations are observed in all branches of science and culture, ranging from the behavior of ele-mentary particles, atoms, molecules in simple chemical or physical systems or even in complex organisms, up to oscillations of the behavior…

Various oscillatory phenomena occur in the world. Because some oscillations are related to abnormal states (e.g., particular diseases), establishing state-transition methods from an oscillatory to a resting state is important. In this…

The "ratchet principle" asserts that non-equilibrium systems which violate parity symmetry generically exhibit steady-state currents. As recently shown, there are exceptions to this principle, due to the existence of hidden time-reversal…

We study a mechanism for reliable switching in biomolecular signal-transduction cascades. Steady bistable states are created by system-size cooperative effects in populations of proteins, in spite of the fact that the phosphorylation-state…