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Interconnecting power systems has a number of advantages such as better electric power quality, increased reliability of power supply, economies of scales through production and reserve pooling and so forth. Simultaneously, it may…
Quantum annealing (QA) is a way to solve combinational optimization problems. Kerr nonlinear parametric oscillators (KPOs) are promising devices for implementing QA. When we solve the combinational optimization problems using KPOs, it is…
The bifurcation structure of coupled periodically driven double-well Duffing oscillators is investigated as a function of the strength of the driving force $f$ and its frequency $\Omega$. We first examine the stability of the steady state…
Cluster states are versatile quantum resources and an essential building block for measurement-based quantum computing. The possibility to generate cluster states in specific systems may thus serve as an indicator regarding if and to what…
As modern engineering systems grow in complexity, attitudes toward a modular design approach become increasingly more favorable. A key challenge to a modular design approach is the certification of robust stability under uncertainties in…
Systems of coupled optical parametric oscillators (OPOs) forming an Ising machine are emerging as large-scale simulators of the Ising model. The advances in computer science and nonlinear optics have triggered not only the physical…
We investigate signatures of quantum chaos in the mixed-field quantum Ising model on finite-size Erd\H{o}s-R\'enyi graphs using probes scalable on near-term quantum devices. By tuning the graph connectivity, the system exhibits a crossover…
We investigate numerically parametrically driven coupled nonlinear Schrodinger equations modelling the dynamics of coupled wavefields in a periodically oscillating double-well potential. The equations describe among other things two coupled…
Collective organisation of patterns into ring-like configurations has been well-studied when patterns are subject to either weak or semi-strong interactions. However, little is known numerically or analytically about their formation when…
We consider the behaviour of a critical system in the presence of a gradient perturbation of the couplings. In the direction of the gradient an interface region separates the ordered phase from the disordered one. We develop a scaling…
We introduce a geometric method for identifying the coupling direction between two dynamical systems based on a bivariate extension of recurrence network analysis. Global characteristics of the resulting inter-system recurrence networks…
Parametric couplings in engineered quantum systems are a powerful tool to control, manipulate and enhance interactions in a variety of platforms. It allows us to bring systems of different energy scales into communication with each other.…
Many studies of synchronization properties of coupled oscillators, based on the classical Kuramoto approach, focus on ensembles coupled via a mean field. Here we introduce a setup of Kuramoto-type phase oscillators coupled via two mean…
Despite recent progress in nonlinear optics in wavelength-scale resonators, there are still open questions on the possibility of parametric oscillation in such resonators. We present a general approach to predict the behavior and estimate…
Having spectral correlations that, over small enough energy scales, are described by random matrix theory is regarded as the most general defining feature of quantum chaotic systems as it applies in the many-body setting and away from any…
We study instabilities and pattern formation in reaction-diffusion layers that are diffusively coupled. For two-layer systems of identical two-component reactions, we analyze the stability of homogeneous steady states by exploiting the…
The analysis of dissipatively coupled oscillators is challenging and highly relevant in power grids. Standard mathematical methods are not applicable, due to the lack of network symmetry induced by dissipative couplings. Here we demonstrate…
Cooperative effects in oscillator networks are often associated with enhanced stability of phase-locked solutions, which increases with system size. We show that the stabilization of persistent currents in annular atomic superfluids with…
We derive a general theory of linear coupling and Kerr nonlinear coupling between modes of dielectric optical resonators from first principles. The treatment is not specific to a particular geometry or choice of mode basis, and can…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…