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The synchronization transition of correlated ensembles of coupled Kuramoto oscillators on sparse random networks is investigated. Extensive numerical simulations show that correlations between the native frequencies of adjacent oscillators…
The synchronization phenomenon is ubiquitous in nature. In ensembles of coupled oscillators, explosive synchronization is a particular type of transition to phase synchrony that is first-order as the coupling strength increases. Explosive…
The Kuramoto model is a classical model used in the study of spontaneous synchronizations in networks of coupled oscillators. In this model, frequency synchronization configurations can be formulated as complex solutions to a system of…
Asymptotic synchronization is one of the essential differences between artificial neural networks and biologically inspired neural networks due to mismatches from dynamical update of weight parameters and heterogeneous activations. In this…
Krotov and Hopfield (2021) proposed a biologically plausible two-layer associative memory network with memory storage capacity exponential in the number of visible neurons. However, the capacity was only linear in the number of hidden…
Synchronization is an omnipresent collective phenomenon in nature and technology, whose understanding is in particular for real-world systems still elusive. We study the synchronization transition in a phase oscillator system with two…
Synchronization is an important phenomenon in a wide variety of systems comprising interacting oscillatory units, whether natural (like neurons, biochemical reactions, cardiac cells) or artificial (like metronomes, power grids, Josephson…
We review our models of quantum associative memories that represent the "quantization" of fully coupled neural networks like the Hopfield model. The idea is to replace the classical irreversible attractor dynamics driven by an Ising model…
The recent discovery of special human neocortical pyramidal neurons that can individually learn the XOR function highlights the significant performance gap between biological and artificial neurons. The output of these pyramidal neurons…
I present a quantum-tunnelling oscillator model as a universal dynamical engine for two paradigmatic problems in quantum cognition theory -- optical illusion perception and group decision making -- where individuals are treated as…
This paper presents a nonlinear control framework for steering networks of coupled oscillators toward desired phase-locked configurations. Inspired by brain dynamics, where structured phase differences support cognitive functions, the focus…
Correlations are employed in modern physics to explain microscopic and macroscopic phenomena, like the fractional quantum Hall effect and the Mott insulator state in high temperature superconductors and ultracold atoms. Simultaneously…
How the brain co-ordinates the actions of distant regions in an efficient manner is an open problem. Many believe that cross-frequency coupling between the amplitude of high frequency local field potential oscillations in one region and the…
We generalize the Kuramoto model for the synchronization transition of globally coupled phase oscillators to populations by incorporating an additional heterogeneity with the coupling strength, where each oscillator pair interacts with…
We extend the theory of weakly coupled oscillators to incorporate slowly varying inputs and parameters. We employ a combination of regular perturbation and an adiabatic approximation to derive equations for the phase-difference between a…
Networked systems have been used to model and investigate the dynamical behavior of a variety of systems. For these systems, different levels of complexity can be considered in the modeling procedure. On one hand, this can offer a more…
Hybrid oscillator architectures that combine feedback oscillators with self-sustained negative resistance oscillators have emerged as a promising platform for artificial neuron design. In this work, we introduce a modeling and analysis…
We investigate the role of the learning rate in a Kuramoto Model of coupled phase oscillators in which the coupling coefficients dynamically vary according to a Hebbian learning rule. According to the Hebbian theory, a synapse between two…
We study synchronization of Kuramoto oscillators in strongly modular networks in which the structure of the network inside each community is averaged. We find that the dynamics of the interacting communities can be described as an ensemble…
Kuramoto networks constitute a paradigmatic model for the investigation of collective behavior in networked systems. Despite many advances in recent years, many open questions remain on the solutions for systems composed of coupled Kuramoto…