相关论文: Optimizing Synchronization Stability of the Kuramo…
In this paper, we propose an $N$ oscillators Kuramoto model with quaternions $\mathbb{H}$. In case the coupling strength is strong, a sufficient condition of synchronization is established for general $N\geqslant 2$. On the other hand, we…
The theoretical description of synchronization phenomena often relies on coupled units of continuous time noisy Markov chains with a small number of states in each unit. It is frequently assumed, either explicitly or implicitly, that…
An optimal control for a dynamical system optimizes a certain objective function. Here we consider the construction of an optimal control for a stochastic dynamical system with a random structure, Poisson perturbations and random jumps,…
The hypothesis, that cortical dynamics operates near criticality also suggests, that it exhibits universal critical exponents which marks the Kuramoto equation, a fundamental model for synchronization, as a prime candidate for an underlying…
A new collective behavior of resonant synchronization is discovered and the ability to retrieve information from brain memory is proposed based on this mechanism. We use modified Kuramoto phase oscillator to simulate the dynamics of a…
A general stability analysis is presented for the determination of the transition from incoherent to coherent behavior in an ensemble of globally coupled, heterogeneous, continuous-time dynamical systems. The formalism allows for the…
Recurrent neural networks (RNNs) with random, but sufficiently strong and balanced coupling display a well known high-dimensional chaotic dynamics. Here, we investigate if externally applied inputs to these RNNs can stabilize globally…
Stochastic resetting has emerged as a powerful mechanism for driving systems into nonequilibrium stationary states with tunable properties. While most existing studies focus on global resetting, where all degrees of freedom are…
We consider the Kuramoto model on sparse random networks such as the Erd\H{o}s-R\'enyi graph or its combination with a regular two-dimensional lattice and study the dynamical scaling behavior of the model at the synchronization transition…
We investigate the dynamics of the adaptive Kuramoto model with slow adaptation in the continuum limit, $N\to\infty$. This model is distinguished by dense multistability, where multiple states coexist for the same system parameters. The…
We introduce a computationally efficient and accurate reduced order modelling approach for the optimization of spatiotemporally chaotic systems. The proposed method combines quantized local reduced order modelling with adjoint-based…
We present a framework for controlling the collective phase of a system of coupled oscillators described by the Kuramoto model under the influence of a periodic external input by combining the methods of dynamical reduction and optimal…
In this article, a new synchronization scheme is presented by combining the concept of reduced-order synchronization with multi-switching synchronization schemes. The presented scheme, reduced-order multi-switching hybrid synchronization,…
The classical Kuramoto model is studied in the setting of an infinite horizon mean field game. The system is shown to exhibit both synchronization and phase transition. Incoherence below a critical value of the interaction parameter is…
One of the simplest mathematical models in the study of nonlinear systems is the Kuramoto model, which describes synchronization in systems from swarms of insects to superconductors. We have recently found a connection between the original,…
Despite growing interest in synchronization dynamics over "higher-order" network models, optimization theory for such systems is limited. Here, we study a family of Kuramoto models inspired by algebraic topology in which oscillators are…
The rapid increase in the integration of intermittent and stochastic renewable energy resources (RER) introduces challenging issues related to power system stability. Interestingly, identifying grid nodes that can best support stochastic…
This paper studies the synchronization of a finite number of Kuramoto oscillators in a frequency-dependent bidirectional tree network. We assume that the coupling strength of each link in each direction is equal to the product of a common…
In this paper, we propose a centralized secondary control for the real-time steady-state optimization of multi-terminal HVdc grids under voltage and current limits. First, we present the dynamic models of the grid components, including the…
Dynamical Ising machines are actively investigated from the perspective of finding efficient heuristics for NP-hard optimization problems. However, the existing data demonstrate super-polynomial scaling of the running time with the system…