Related papers: Resonant synchronization and information retrieve …
The higher-order interactions of complex systems, such as the brain are captured by their simplicial complex structure and have a significant effect on dynamics. However, the existing dynamical models defined on simplicial complexes make…
Associative memory systems enable content-addressable storage and retrieval of patterns, a capability central to biological neural computation and artificial intelligence. Classical implementations such as Hopfield networks face fundamental…
We investigate in depth the synchronization of coupled oscillators on top of complex networks with different degrees of heterogeneity within the context of the Kuramoto model. In a previous paper [Phys. Rev. Lett. 98, 034101 (2007)], we…
Synchronization is a fundamental phenomenon in complex systems, observed across a wide range of natural and engineered contexts. The Kuramoto model provides a foundational framework for understanding synchronization among coupled…
Recently, there has been significant advancement in the machine learning (ML) approach and its application to diverse systems ranging from complex to quantum systems. As one of such systems, a coupled-oscillators system exhibits intriguing…
Partial, instead of complete, synchronization has been widely observed in various networks including, in particular, brain networks. Motivated by data from human brain functional networks, in this technical note, we analytically show that…
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…
The features of animal population dynamics, for instance, flocking and migration, are often synchronized for survival under large-scale climate change or perceived threats. These coherent phenomena have been explained using synchronization…
The experimental study of neural networks requires simultaneous measurements of a massive number of neurons, while monitoring properties of the connectivity, synaptic strengths and delays. Current technological barriers make such a mission…
Globally coupled ensembles of phase oscillators serve as useful tools for modeling synchronization and collective behavior in a variety of applications. As interest in the effects of simplicial interactions (i.e., non-additive, higher-order…
In the field of collective dynamics, the Kuramoto model serves as a benchmark for the investigation of synchronization phenomena. While mean-field approaches and complex networks have been widely studied, the simple topology of a circle is…
Networks incorporating higher-order interactions are increasingly recognized for their ability to introduce novel dynamics into various processes, including synchronization. Previous studies on synchronization within multilayer networks…
Systems of mobile physical entities exchanging information with their neighborhood can be found in many different situations. The understanding of their emergent cooperative behaviour has become an important issue across disciplines,…
The emergence of explosive synchronization has been reported as an abrupt transition in complex networks of first-order Kuramoto oscillators. In this Letter, we demonstrate that the nodes in a second-order Kuramoto model, perform a cascade…
We consider a toy model of two kinetically coupled stochastic oscillators whose dynamics is described as a Markov jump process among $N$ discrete phase states. For large $N$, it maps onto the deterministic two-oscillator Kuramoto model of…
The Kuramoto model is a system of nonlinear differential equations that models networks of coupled oscillators and is often used to study synchronization among them. It has been observed that if the natural frequencies of the oscillators…
A wide variety of engineered and natural systems are modelled as networks of coupled nonlinear oscillators. In nature, the intrinsic frequencies of these oscillators are not constant in time. Here, we probe the effect of such a temporal…
The Kuramoto model is a classical mathematical model in the field of non-linear dynamical systems that describes the evolution of coupled oscillators in a network that may reach a synchronous state. The relationship between the network's…
Synchronization occurs in many natural and technological systems, from cardiac pacemaker cells to coupled lasers. In the synchronized state, the individual cells or lasers coordinate the timing of their oscillations, but they do not move…
Associative memory models retrieve stored information through content-based addressing, mimicking the neural processes of animal brains. The classical Hopfield network-based models store memories as vectors of discrete values and have good…