Related papers: Slow oscillating dynamics of a two-level system su…
We study the dynamics of networks with coupling delay, from which the connectivity changes over time. The synchronization properties are shown to depend on the interplay of three time scales: the internal time scale of the dynamics, the…
We present a systematic study of moment evolution in multidimensional stochastic difference systems, focusing on characterizing systems whose low-order moments diverge in the neighborhood of a stable fixed point. We consider systems with a…
We investigate the transient evolution of finite-frequency current noise after abrupt switching on of the tunneling coupling in two paradigmatic, exactly solvable models of mesoscopic physics: the resonant level model and the Majorana…
The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a…
Noise and spatial degrees of freedom characterize most ecosystems. Some aspects of their influence on the coevolution of populations with cyclic interspecies competition have been demonstrated in recent experiments [e.g. B. Kerr et al.,…
We examine a model of two interacting populations of phase oscillators labelled `Blue' and `Red'. To this we apply tempered stable L\'{e}vy noise, a generalisation of Gaussian noise where the heaviness of the tails parametrised by a power…
We show that the dipole, a system usually proposed to model relaxation phenomena, exhibits a maximum in the signal-to-noise ratio at a non-zero noise level, thus indicating the appearance of stochastic resonance. The phenomenon occurs in…
In this letter we present a stochastic dynamic model which can explain economic cycles. We show that the macroscopic description yields a complex dynamical landscape consisting of multiple stable fixed points, each corresponding to a split…
A natural phenomenon occurring in a living system is an outcome of the dynamics of the specific biological network underlying the phenomenon. The collective dynamics have both deterministic and stochastic components. The stochastic nature…
Superconducting circuits are a leading platform for quantum computing. However, their coherence times are still limited and exhibit temporal fluctuations. Those phenomena are often attributed to the coupling between qubits and material…
We investigate the dynamics of the voter model in which the population itself changes endogenously via the birth-death process. There are two species of voters, labeled A and B, and the population of each species can grow or shrink by the…
This is the transcript of a talk given at the 1992 Complex Systems Summer School. The theory of large fluctuations of stochastically perturbed continuous-time dynamical systems is reviewed, and the large fluctuations of two stochastic…
Fluctuation scaling is observed phenomenon from complex networks through finance to ecology. It means that the variance and the mean of a specific quantity are related as $\ev{\sigma^2|n}\propto \ev{n|A}^{2\alpha}$ with $1/2\geq \alpha \geq…
Stochastic phenomena in which the noise amplitude is proportional to the fluctuating variable itself, usually called {\it multiplicative noise}, appear ubiquitously in physics, biology, economy and social sciences. The properties of…
We study dynamical decoupling of a qubit from non gaussian quantum noise due to discrete sources, as bistable fluctuators and 1/f noise. We obtain analytic and numerical results for generic operating point. For very large pulse frequency,…
The dynamics of living systems often serves the purpose of reaching functionally important target states. We previously proposed a theory to analyze stochastic biological dynamics evolving towards target states in reverse time. However, a…
Competition is the main driver of population dynamics, which shapes the genetic composition of populations and the assembly of ecological communities. Neutral models assume that all the individuals are equivalent and that the dynamics is…
We continue the work of a series of previous studies of a mathematical model that describes the mean-field limit behavior of a homogeneous network of excitatory point spiking neurons. Contrary to other models, here noise is intrinsic to the…
Population dynamics reflects an underlying birth-death process, where the rates associated with different events may depend on external environmental conditions and on the population density. A whole family of simple and popular…
We study steady-state dynamic fluctuations of current and mass, as well as the corresponding power spectra, in conserved-mass transport processes on a ring of $L$ sites; these processes violate detailed balance, have nontrivial spatial…