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Stochastic resonance holds much promise for the detection of weak signals in the presence of relatively loud noise. Following the discovery of nondynamical and of aperiodic stochastic resonance, it was recently shown that the phenomenon can…
The synchronization stability of a complex network system of coupled phase oscillators is discussed. In case the network is affected by disturbances, a stochastic linearized system of the coupled phase oscillators may be used to determine…
Electricity systems are experiencing increased effects of randomness and variability due to emerging stochastic assets. The increased effects introduce new uncertainties into power systems that can impact system operability and reliability.…
Stochastic motion of particles in a highly unstable potential generates a number of diverging trajectories leading to undefined statistical moments of the particle position. This makes experiments challenging and breaks down a standard…
Using a simple model, we study the fluctuating dynamics of inextensible, semiflexible polar filaments interacting with active and directed force generating centres such as molecular motors. Taking into account the fact that the activity…
In real-world applications, observations are often constrained to a small fraction of a system. Such spatial subsampling can be caused by the inaccessibility or the sheer size of the system, and cannot be overcome by longer sampling.…
Our observations of the quiet Sun with the NST have yielded unanticipated results on smal-scale solar dynamic. Althought small-scale solar dynamic have been well-studied, the NST is enabling us to probe finer scale dynamic exploiting higher…
In the paper below we consider a problem of stabilization of a priori unknown unstable periodic orbits in non-linear autonomous discrete dynamical systems. We suggest a generalization of a non-linear DFC scheme to improve the rate of…
The incorporation of uncertainties to calculations of signal significance in planned experiments is an actual task. Several approaches to this problem are discussed. We present a procedure for taking into account the systematic uncertainty…
It is possible that self-induced oscillations appear in reactors, and that their range does not reach the steady state, although such state exists. To prove this, a cascade of tank reactors coupled with mass recycle loop was tested…
Many interesting phenomena in nature are described by stochastic processes with irreversible dynamics. To model these phenomena, we focus on a master equation or a Fokker-Planck equation with rates which violate detailed balance. When the…
The solar magnetic activity consists of two periodic components: the main cycle with a period of 11 yr and a shorter cycle with a period of ~2 yrs. The origin of this second periodicity is still not well understood. We use almost 15 yrs of…
The power spectral density of an observable quantifies the amount of fluctuations at a given frequency and can reveal the influence of different timescales on the observable's dynamics. Here, we show that the spectral density in a…
Observations show that the solar p-mode frequencies change with the solar cycle. The horizontal-phase-velocity dependence of the relative frequency change, scaled by mode mass, provides depth information on the perturbation in the solar…
The solar cycle and its associated magnetic activity are the main drivers behind changes in the interplanetary environment and Earth's upper atmosphere (commonly referred to as space weather and climate). In recent years there has been an…
The scattering of coherent X-rays from dynamically evolving systems is currently becoming experimentally feasible. The scattered beam produces a pattern of bright and dark speckles, which fluctuate almost independently in time and can be…
We consider a nonlinear pendulum whose suspension point undergoes stochastic vibrations in its plane of motion. Stochastic vibrations are constructed by stochastic differential equations with random periodic solutions. Averaging over these…
Solar variability occurs over a broad range of spatial and temporal scales, from the Sun's brightening over its lifetime to the fluctuations commonly associated with magnetic activity over minutes to years. The latter activity includes most…
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 investigate the variability properties of main sequence stars in the first month of Kepler data, using a new astrophysically robust systematics correction, and find that 60% of stars are more variable then the active Sun. We define low…