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In this paper we propose a hybrid model of a neural oscillator, obtained by partially discretizing a well-known continuous model. Our construction points out that in this case the standard techniques, based on replacing sigmoids with step…
Traditional artificial neural networks consist of nodes with non-oscillatory dynamics. Biological neural networks, on the other hand, consist of oscillatory components embedded in an oscillatory environment. Motivated by this feature of…
Algorithms for associative memory typically rely on a network of many connected units. The prototypical example is the Hopfield model, whose generalizations to the quantum realm are mainly based on open quantum Ising models. We propose a…
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…
An open problem in neuroscience is to explain the functional role of oscillations in neural networks, contributing, for example, to perception, attention, and memory. Cross-frequency coupling (CFC) is associated with information integration…
Coupled oscillators have been used to study synchronization in a wide range of social, biological, and physical systems, including pedestrian-induced bridge resonances, coordinated lighting up of firefly swarms, and enhanced output peak…
In this paper we study robust synchronization of time-fractional Hopfield neural networks with memristive couplings and Hebbian learning rules. This new model of artificial neural networks exhibits strong memory and long-range…
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…
We introduce a novel coupling scheme for maximizing the synchronization of Kuramoto oscillator networks under a fixed coupling budget. We show that by scaling the interaction strength between oscillators according to their frequency…
We investigate the engineering scenario where the objective is to synchronize heterogeneous oscillators in a distributed fashion. The internal dynamics of each oscillator are general enough to capture their time-varying natural frequency as…
Artificial neural networks are intensively used to perform cognitive tasks such as image classification on traditional computers. With the end of CMOS scaling and increasing demand for efficient neural networks, alternative architectures…
The classical Kuramoto model consists of finitely many pairwise coupled oscillators on the circle. In many applications a simple pairwise coupling is not sufficient to describe real-world phenomena as higher-order (or group) interactions…
In this work we study the synchronization of Kuramoto oscillators driven by external forces in complex modular networks. The motivation is the neuronal dynamics that takes place during information processing in the neural cortex. The neuron…
Designing high-performing networks requires optimizing for functionality while respecting physical, geometric, or budget constraints. Yet, mathematical and computational tools to design such systems remain limited, particularly for…
The conditions under which synchronization is achieved for a one-dimensional ring of identical phase oscillators with Kuramoto-like local coupling are studied. The system is approached in the weakly coupled approximation as phase units.…
The Kuramoto model is a standard model for the dynamics of coupled oscillator networks. In particular, it is used to study long time behavior such as phase-locking where all oscillators rotate at a common frequency with fixed angle…
Circuits of biological neurons, such as in the functional parts of the brain can be modeled as networks of coupled oscillators. Inspired by the ability of these systems to express a rich set of outputs while keeping (gradients of) state…
A large number of neural network models of associative memory have been proposed in the literature. These include the classical Hopfield networks (HNs), sparse distributed memories (SDMs), and more recently the modern continuous Hopfield…
Simplicial Kuramoto models have emerged as a diverse and intriguing class of models describing oscillators on simplices rather than nodes. In this paper, we present a unified framework to describe different variants of these models,…
Quantum-like (QL) modeling, one of the outcomes of the quantum information revolution, extends quantum theory methods beyond physics to decision theory and cognitive psychology. While effective in explaining paradoxes in decision making and…