Related papers: The parametric instability landscape of coupled Ke…

We study parametric oscillations of two capacitively coupled Kerr parametric oscillators (KPOs) with frequency-chirped two- and one-photon drives. The two-KPO system adiabatically evolves from the initial vacuum state to an oscillation…

We study parametrically driven quantum oscillators and show that, even for weak coupling between the oscillators, they can exhibit various many-body states with broken time-translation symmetry. In the quantum-coherent regime, the symmetry…

Cascading failures in complex systems have been studied extensively using two different models: $k$-core percolation and interdependent networks. We combine the two models into a general model, solve it analytically and validate our…

Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…

This thesis is mainly devoted to the study of the quantum properties of optical parametric oscillators (OPOs), which are nowadays the sources of the highest-quality quantum-correlated light, apart from fundamental tools in the…

We study systems of coupled units in a general network configuration with a coupling delay. We show that the destabilizing bifurcations from an equilibrium are governed by the extreme eigenvalues of the coupling matrix of the network. Based…

The growing challenges of scaling digital computing motivate new approaches, especially through the dynamical evolution of physical systems that mimic neural networks and combinatorial optimization problems. While light is a hyper efficient…

Bifurcation analysis collects techniques for characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Common solution classes of interest include equilibria and periodic…

A system of nearest neighbors Kuramoto-like coupled oscillators placed in a ring is studied above the critical synchronization transition. We find a richness of solutions when the coupling increases, which exists only within a solvability…

We consider networks of coupled stochastic oscillators. When coupled we find strong collective oscillations, while each unit remains stochastic. In the limit (N\to \infty) we derive a system of integro-delay equations and show analytically…

We study the response of an optical system with the Kerr nonlinearity demonstrating Bloch oscillations to a periodic train of coherent pulses. It has been found out that the intensity of the field excited in the system by pulses resonantly…

We investigate the existence and stability of travelling wave solutions in a continuum field of non-locally coupled identical phase oscillators with distance-dependent propagation delays. A comprehensive stability diagram in the parametric…

We identify persistent oscillations in a nonintegrable quantum Ising chain. In the integrable chain with nearest-neighbor interactions, the nature, origin, and decay of post-transition oscillations are tied to the Kibble-Zurek mechanism.…

Formation of chaos in the parametric dependent system of interacting oscillators for the both classical and quantum cases has been investigated. Domain in which classical motion is chaotic is defined. It has been shown that for certain…

Parametrically driven oscillators provide a natural platform for neuromorphic computation, where nonlinear mode coupling and intrinsic dynamics enable both memory and high-dimensional transformation. Here, we investigate a two-mode system…

Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability…

Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems, but have not been fully explored in high-dimensional networks. Here we study large networks…

We propose that neuromorphic computing can perform quantum operations. Spiking neurons in the active or silent states are connected to the two states of Ising spins. A quantum density matrix is constructed from the expectation values and…

Parametrized quantum circuits are essential components of variational quantum algorithms. Until now, optical implementations of these circuits have relied solely on adjustable linear optical units. In this study, we demonstrate that using…

We study a tripartite system of coupled spins, where a first set of one or two spins is our central system which is coupled to another set considered, the near environment, in turn coupled to the third set, the far environment. The dynamics…