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We study singularly perturbed systems that exhibit input-to-state stability (ISS) with fixed-time properties in the presence of bounded disturbances. In these systems, solutions converge to the origin within a time frame independent of…
This paper is devoted to show the results obtained by using the magnitude-squared coherence for determining order-chaos transition in a system described by the logistic equation dynamics. For determining the power spectral density of a…
Imbalanced and small data regimes are pervasive in domains such as rare disease imaging, genomics, and disaster response, where labeled samples are scarce and naive augmentation often introduces artifacts. Existing solutions such as…
This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…
In the last decade it has been shown that a large class of phase oscillator models admit low dimensional descriptions for the macroscopic system dynamics in the limit of an infinite number N of oscillators. The question of whether the…
While a previously proposed method for estimating inertial manifold dimension, based on explicitly computing angles between pairs of covariant Lyapunov vectors (CLVs), employs efficient algorithms, it remains computationally demanding due…
This paper advances the stochastic regularity theory for the Navier-Stokes equations by introducing a variable-intensity noise model within the Sobolev and Besov spaces. Traditional models usually assume constant-intensity noise, but many…
This paper develops new variance-reduction techniques for the forward-reflected-backward splitting (FRBS) method to solve a class of possibly nonmonotone stochastic composite inclusions. Unlike unbiased estimators such as mini-batching,…
In an acoustic cavity with a heat source, such as a flame in a gas turbine, the thermal energy of the heat source can be converted into acoustic energy, which may generate a loud oscillation. If uncontrolled, these nonlinear acoustic…
Stochastic partial differential equations have been used in a variety of contexts to model the evolution of uncertain dynamical systems. In recent years, their applications to geophysical fluid dynamics has increased massively. For a…
We develop a powerful and general method to provide rigorous and accurate upper and lower bounds for Lyapunov exponents of stochastic flows. Our approach is based on computer-assisted tools, the adjoint method and established results on the…
This paper presents novel adaptive space-time reduced-rank interference suppression least squares algorithms based on joint iterative optimization of parameter vectors. The proposed space-time reduced-rank scheme consists of a joint…
The aim of this paper is to provide a novel systematic methodology for the design of sampled-data observers for Linear Kuramoto-Sivashinsky systems (LK-S) with non-local outputs. More precisely, we extend the systematic sampled-data…
To tackle the curse of dimensionality and multicollinearity problems of polynomial chaos expansion for analyzing global sensitivity and reliability of models with high stochastic dimensions, this paper proposes a novel non-intrusive…
Fourier transform-based methods enable accurate, dispersion-free simulations of time-domain scattering problems by evaluating solutions to the Helmholtz equation at a discrete set of frequencies sufficient to approximate the inverse Fourier…
Scientists have been considering the Kuramoto model to understand the mechanism behind the appearance of collective behaviour, such as frequency synchronisation (FS) as a paradigm, in real-world networks with a finite number of oscillators.…
We first propose the concept of Stepanov-like weighted pseudo-almost automorphic on time-space scales and we apply this type of oscillation to high-order BAM neural networks with mixed delays. Then, we study the existence and exponential…
We consider the problem of global stability of nonlinear sampled-data systems. Sampled-data systems are a form of hybrid model which arises when discrete measurements and updates are used to control continuous-time plants. In this paper, we…
We consider a Kuramoto-Shivashinsky like equation close to the threshold of instability with additive white noise and spatially periodic boundary conditions which simultaneously exhibit Turing bifurcations with a spatial 1:3 resonance of…
Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract…