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The parameterization method (PM) provides a broad theoretical and numerical foundation for computing invariant manifolds of dynamical systems. PM implements a change of variables in order to represent trajectories of a system of ordinary…
A universal mechanism underlying generalized synchronization conditions in unidirectionally coupled stochastic oscillators is considered. The consideration is carried out in the framework of a modified system with additional dissipation.…
We revisit the phenomenon of quantum stochastic resonance in the regime of validity of the Bloch equations. We find that a stochastic resonance behavior in the steady-state response of the system is present whenever the noise-induced…
Thomas and Lindner (2014, Phys.Rev.Lett.) defined an asymptotic phase for stochastic oscillators as the angle in the complex plane made by the eigenfunction, having a complex eigenvalue with a least negative real part, of the backward…
In networked systems, stochastic resonance occurs as a collective phenomenon where the entire stochastic network resonates with a weak applied periodic signal. Beyond the interplay among the network coupling, the amplitude of the external…
Many physical, chemical and biological processes rely on intrinsic oscillations to employ resonance responses to external stimuli of certain frequency. Such resonance phenomena in biological systems are typically explained by one of two…
We consider a stochastically forced nonlinear oscillator driven by a stationary Gaussian noise that has an algebraically decaying covariance function. It is well known that such noise processes can be renormalized to converge to fractional…
The mechanism of stochastic electron acceleration in colliding laser waves is investigated by employing proper canonical variables and effective time, such that the new Hamiltonian becomes time independent when the perturbative (weaker)…
A fluctuation theory is presented for the nonequilibrium second order phase transition in a quasi-two-dimensional electron gas. A transverse (with respect to the current through the sample) spontaneous electric field as an order parameter…
We consider a Brownian oscillator whose coupling to the environment may lead to the formation of a localized normal mode. For lower values of the oscillator's natural frequency, $\omega\le\omega_c$, the localized mode is absent and the…
Many nonlinear systems are described by eigenmodes with amplitude-dependent frequencies, interacting strongly whenever the frequencies become commensurate at internal resonances. Fast energy exchange via the resonances holds the key to rich…
The interplay of such cornerstones of modern nonlinear fiber optics as a nonlinearity, stochasticity and polarization leads to variety of the noise induced instabilities including polarization attraction and escape phenomena harnessing of…
The interaction of electromagnetic radiation with temporally dispersive magnetic solids of small dimensions may show very special resonant behaviors. The internal fields of such samples are characterized by magnetostatic-potential scalar…
We have analyzed the effects of the addition of external noise to non-dynamical systems displaying intrinsic noise, and established general conditions under which stochastic resonance appears. The criterion we have found may be applied to a…
Stochastic resonance is a well established phenomenon, which proves relevant for a wide range of applications, of broad trans-disciplinary breath. Consider a one dimensional bistable stochastic system, characterized by a deterministic…
Stochastic resonance is a phenomenon where a noise of appropriate intensity enhances the input signal strength. In this work, by employing the recently developed convex optimization methods in the context of dynamical systems and stochastic…
We study the phenomenon of nonlinear stochastic resonance (SR) in a complex noisy system formed by a finite number of interacting subunits driven by rectangular pulsed time periodic forces. We find that very large SR gains are obtained for…
The article describes fundamental analytical properties of an unforced mechanical oscillator with a Duhem-type viscoelastoplastic hysteretic element. These properties include global existence of solutions, uniqueness of solutions, and…
We carry out a detailed numerical investigation of stochastic resonance in underdamped systems in the non-perturbative regime. We point out that an important distinction between stochastic resonance in overdamped and underdamped systems…
We study long-range interacting systems driven by external stochastic forces that act collectively on all the particles constituting the system. Such a scenario is frequently encountered in the context of plasmas, self-gravitating systems,…