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A new algorithm is presented for reconstructing stochastic nonlinear dynamical models from noisy time-series data. The approach is analytical; consequently, the resulting algorithm does not require an extensive global search for the model…
We investigate the behavior of the residence times density function for different nonlinear dynamical systems with limit cycle behavior and perturbed parametrically with a colored noise. We present evidence that underlying the stochastic…
Recently, time scales calculus is developed to unify continuous and discrete analysis. By extending the definition of time scales properly, this paper introduces the concept of a signal set as well as its stability properties in terms of…
The concept of stochastic resonance in nonlinear dynamics is applied to interpret the capacity of noisy quantum channels. The two-Pauli channel is used to illustrate the idea. The fidelity of the channel is also considered. Noise…
Many neuronal systems and models display a certain class of mixed mode oscillations (MMOs) consisting of periods of small amplitude oscillations interspersed with spikes. Various models with different underlying mechanisms have been…
Noisy monitored quantum circuits have emerged as a versatile and unifying framework connecting quantum many-body physics, quantum information, and quantum computation. In this review, we provide a comprehensive overview of recent advances…
Recent research on the dynamics of certain fluid dynamical instabilities shows that when there is a slow invariant manifold subject to fast timescale instability the dynamics are extremely sensitive to noise. The behaviour of such systems…
We consider the problem of parameter estimation, based on noisy chaotic signals, from the viewpoint of twisted modulation for waveform communication. In particular, we study communication systems where the parameter to be estimated is…
We make use of the formalism described in a previous paper [Martins {\it et al.} Phys. Rev. D90 (2014) 043518] to address general features of wiggly cosmic string evolution. In particular, we highlight the important role played by poorly…
Partitioning large networks into stable clusters of synchronized nodes is a challenging task. Recent approaches based on spectral analysis can provide exact results on specific dynamics but remain unfeasible for very large networks.…
Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…
We demonstrate the phenomenon of stochastic resonance (SR) for discrete-time dynamical systems. We investigate various systems that are not necessarily bistable, but do have two well defined states, switching between which is aided by…
We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…
Nonequilibrium many-body transient dynamics play an important role in the adaptation of active matter systems environment changes. However, the generic universal behavior of such dynamics is usually elusive and left as open questions. Here,…
In this paper, we give estimators of the frequency, amplitude and phase of a noisy sinusoidal signal with time-varying amplitude by using the algebraic parametric techniques introduced by Fliess and Sira-Ramirez. We apply a similar strategy…
Impulsive systems are a very flexible class of systems that can be used to represent switched and sampled-data systems. We propose to extend here the previously obtained results on deterministic impulsive systems to the stochastic setting.…
The emergent dynamics of complex systems often arise from the internal dynamical interactions among different elements and hence is to be modeled using multiple variables that represent the different dynamical processes. When such systems…
Previous preliminary results on the application of knowledge networks to noise reduction in stationary harmonic and weakly chaotic signals are extended to more general cases. The formalism gives a novel algorithm from which statistical…
Recent research has shown that performance in signal processing tasks can often be significantly improved by using signal models based on sparse representations, where a signal is approximated using a small number of elements from a fixed…
We study the role of multiplicative colored noise for different values of the correlation time $\tau_c$ in the dynamics of two competing species, described by generalized Lotka-Volterra equations. The multiplicative colored noise models the…