Related papers: A Note on Analyzing the Stability of Oscillator Is…
Networks of coupled nonlinear oscillators can display a wide range of emergent behaviours under variation of the strength of the coupling. Network equations for pairs of coupled oscillators where the dynamics of each node is described by…
Hyperexponential stability is investigated for dynamical systems with the use of both, explicit and implicit, Lyapunov function methods. A nonlinear hyperexponential control is designed for stabilizing linear systems. The tuning procedure…
In this work the existence of periodic solutions is studied for the Hamiltonian functions (Formula presented.) where the first term consist of a harmonic oscillator and the second term are homogeneous polynomials of degree 5 defined by two…
We study large networks of parametric oscillators as heuristic solvers of random Ising models. In these networks, known as coherent Ising machines, the model to be solved is encoded in the coupling between the oscillators, and a solution is…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
It is challenging to scale Ising machines for industrial-level problems due to algorithm or hardware limitations. Although higher-order Ising models provide a more compact encoding, they are, however, hard to physically implement. This work…
We propose a novel algorithm for testing the hypothesis of nonstationarity in complex-valued signals. The implementation uses both the bootstrap and the Fast Fourier Transform such that the algorithm can be efficiently implemented in…
Potential disagreement in the result induced by discontinuities is revealed in this paper between a novel power system transient simulation scheme using numerical integrators considering second order derivative and conventional ones using…
For a class of coupled limit cycle oscillators, we give a condition on a linear coupling operator that is necessary and sufficient for exponential stability of the synchronous solution. We show that with certain modifications our method of…
An approach to stabilization of control systems with ultimately wide ranges of uncertainly disturbed parameters is offered. The method relies on using of nonlinear structurally stable functions from catastrophe theory as controllers.…
This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large…
The commercial and industrial demand for the solution of hard combinatorial optimization problems push forward the development of efficient solvers. One of them is the Ising machine which can solve combinatorial problems mapped to Ising…
Large systems of coupled oscillators subjected to a periodic external drive occur in many situations in physics and biology. Here the simple, paradigmatic case of equal-strength, all-to-all sine-coupling of phase oscillators subject to a…
We consider optimization algorithms that are open systems, that is, with external inputs and outputs. Such algorithms arise for instance, when analyzing the effect of noise or disturbance on an algorithm, or when an algorithm is part of…
Starting from a microscopic theory, we derive a master equation for a harmonic oscillator coupled to a bath of non-interacting oscillators. We follow a non-perturbative approach, proposed earlier by us for the free Brownian particle. The…
Efficient and energy stable high order time marching schemes are very important but not easy to construct for the study of nonlinear phase dynamics. In this paper, we propose and study two linearly stabilized second order semi-implicit…
The linear stability of two exact stationary solutions of the parametrically driven, damped nonlinear Dirac equation is investigated. Stability is ascertained through the resolution of the eigenvalue problem, which stems from the…
High-performance Ising machines for solving combinatorial optimization problems have been developed with digital processors implementing heuristic algorithms such as simulated bifurcation (SB). Although Ising machines have been designed for…
This paper introduces an algorithmic approach to the analysis of Jacobi stability of systems of second order ordinary differential equations (ODEs) via the Kosambi--Cartan--Chern (KCC) theory. We develop an efficient symbolic program using…
In this paper we review recent work on novel computing paradigms using coupled oscillatory dynamical systems. We explore systems of relaxation oscillators based on linear state transitioning devices, which switch between two discrete states…