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The influence of multiplicative white noise on the resonance capture of strongly nonlinear oscillatory systems under chirped-frequency excitations is investigated. It is assumed that the intensity of the perturbation decays polynomially…
Wave self-focusing in molecular systems subject to thermal effects, such as thin molecular films and long biomolecules, can be modeled by stochastic versions of the Discrete Self-Trapping equation of Eilbeck, Lomdahl and Scott, and this can…
Cavity optomechanical systems in the quantum regime consist of a cavity mode and mechanical element coupled together through radiation pressure. In the nonlinear optomechanical regime, open-system dynamics is generally challenging to treat…
We propose a comprehensive dynamical model for cooperative motion of self-propelled particles, e.g., flocking, by combining well-known elements such as velocity-alignment interactions, spatial interactions, and angular noise into a unified…
Nonreciprocal coupling can alter the transport properties of material media, producing striking phenomena such as unidirectional amplification of waves, boundary modes, or self-assembled pattern formation. It is responsible for nonlinear…
We theoretically evaluate the impact of drift-free noise on the dynamics of $\mathcal{PT}$-symmetric non-Hermitian systems with an exceptional point, which have recently been proposed for sensors. Such systems are currently considered as…
Non-Hermitian (NH) photonic systems leverage gain and loss to open new directions for nanophotonic technologies. However, the quantum and thermal noise intrinsically associated with gain/loss affects the eigenvalue/eigenvector structure of…
In this thesis we aim to analyze and quantify the energetic and information contents that can be extracted from a dynamical system subject to the external environment. The latter is usually assumed to be deleterious for the feasibility of…
Plastic rearrangements play a crucial role in the characterization of soft-glassy materials, such as emulsions and foams. Based on numerical simulations of soft-glassy systems, we study the dynamics of plastic rearrangements at the…
Noise fundamentally limits the performance and predictive capabilities of classical and quantum dynamical systems by degrading stability and obscuring intrinsic dynamical characteristics. Characterizing such noise accurately is essential…
Biological systems often consist of a small number of constituents and are therefore inherently noisy. To function effectively, these systems must employ mechanisms to constrain the accumulation of noise. Such mechanisms have been…
In the paper we investigate a mathematical model describing the growth of tumor in the presence of immune response of a host organism. The dynamics of tumor and immune cells is based on the generic Michaelis-Menten kinetics depicting…
Unconventional properties of non-Hermitian systems, such as the existence of exceptional points, have recently been suggested as a resource for sensing. The impact of noise and utility in quantum regimes however remains unclear. In this…
Explosive particle production due to parametric resonance is a crucial feature of reheating in an inflationary cosmology. Coherent oscillations of the inflaton field lead to a periodically varying mass in the evolution equation of matter…
We analyze the effects of noise on the traveling wave dynamics in neural fields. The noise influences the dynamics on two scales: first, it causes fluctuations in the wave profile, and second, it causes a random shift in the phase of the…
Unraveling real eigenfrequencies in non-Hermitian $\mathcal{PT}$-symmetric Hamiltonians has opened new avenues in quantum physics, photonics, and most recently, phononics. However, the existing literature squarely focuses on exploiting such…
Nonlinear dynamical systems possessing reflection symmetry have an invariant subspace in the phase space. The dynamics within the invariant subspace can be random or chaotic. As a system parameter changes, the motion transverse to the…
The non-Hermitian skin effect and nonreciprocal behavior are sensitive to the boundary conditions, which are unique features of non-Hermitian systems. The eigenenergies will become complex and all eigenstates are localized at the boundary,…
A parabolic stochastic PDE is studied analytically and numerically, when a bifurcation parameter is slowly increased through its critical value. The aim is to understand the effect of noise on delayed bifurcations in systems with spatial…
The full dynamics of a synchronous recurrent neural network model with Ising binary units and a Hebbian learning rule with a finite self-interaction is studied in order to determine the stability to synaptic and stochastic noise of…