Related papers: Transient amplification in balanced neural network…
We show how the recurrence phenomenon characteristic of the nonlinear stage of induced modulational instability in a passive fiber is affected by forcing. An additional linear amplification, even if extremely weak, induces separatrix…
Non-normal transient growth of disturbances is considered as an essential prerequisite for subcritical transition in shear flows, i.e. transition to turbulence despite linear stability of the laminar flow. In this work we present numerical…
A study of statistics of transmission and reflection from a random medium with stochastic amplification as opposed to coherent amplification is presented. It is found that the transmission coefficient $t$, for sample length $L$ less than…
Aggregations are emergent features common to many biological systems. Mathematical models to understand their emergence are consequently widespread, with the aggregation-diffusion equation being a prime example. Here we study the…
Population structure has been known to substantially affect evolutionary dynamics. Networks that promote the spreading of fitter mutants are called amplifiers of natural selection, and those that suppress the spreading of fitter mutants are…
A discrete stochastic process involving random amplification with additive noise is studied analytically. If the non-negative random amplification factor $b$ is such that $<b^{\beta}>=1$ where $\beta$ is any positive non-integer, then the…
Many complex networks are known to exhibit sudden transitions between alternative steady states with contrasting properties. Such a sudden transition demonstrates a network's resilience, which is the ability of a system to persist in the…
Heavy-tailed fluctuations and power law distributions pervade physics, biology, and the social sciences, with numerous mechanisms proposed for their emergence. Kesten processes, which are multiplicative stochastic recursions with additive…
Ever since the Barab\'{a}si-Albert (BA) scale-free network has been proposed, network modeling has been studied intensively in light of the network growth and the preferential attachment (PA). However, numerous real systems are featured…
The statistical analysis of the fading End to End channel gain of the amplify and forward relaying protocol, however, is well known as extremely complex, and research work to date have only studied the asymptotic behaviour of the outage…
We study the dynamics of a qubit-resonator system, when the resonator is driven by two signals. The interaction of the qubit with the high-amplitude driving we consider in terms of the qubit dressed states. Interaction of the dressed qubit…
Spreading phenomena on networks are essential for the collective dynamics of various natural and technological systems, from information spreading in gene regulatory networks to neural circuits or from epidemics to supply networks…
We consider a wireless sensor network that uses inductive near-field coupling for wireless powering or communication, or for both. The severely limited range of an inductively coupled source-destination pair can be improved using resonant…
The transmissivity of a one-dimensional random system that is periodic on average is studied. It is shown that the transmission coefficient for frequencies corresponding to a gap in the band structure of the average periodic system…
We study the change in the resurgent asymptotic properties of a trans-series in two parameters, a coupling $g^2$ and a gauge index $N$, as a system passes through a large $N$ phase transition, using the universal example of the…
We report a detailed and systematic numerical study of wave propagation through a coherently amplifying random one-dimensional medium. The coherent amplification is modeled by introducing a uniform imaginary part in the site energies of the…
The amplitude of fluctuation-induced patterns might be expected to be proportional to the strength of the driving noise, suggesting that such patterns would be difficult to observe in nature. Here, we show that a large class of…
The renormalization method based on the Newton-Maclaurin expansion is applied to study the transient behavior of the solutions to the difference equations as they tend to the steady-states. The key and also natural step is to make the…
Transient stability is crucial to the reliable operation of power systems. Existing theories rely on the simplified electromechanical models, substituting the detailed electromagnetic dynamics of inductor and capacitor with their impedance…
We study the limitations on observing transient amplification in atomic systems exhibiting electromagnetically induced transparency (EIT) and evaluate the limits of optical Bloch equation (OBE) models. Using propagation-based Maxwell-Bloch…