27 citations · 65 across the 18 of their papers we have counts for
18 papers
Phase-delays shape multistability and basin sizes in Kuramoto networks: analytical estimates from network structure
Kalel L. Rossi, Antonio Mihara, Lyle E. Muller +2
We study how network connectivity and heterogeneous phase-delays shape the spatiotemporal dynamics of finite oscillator networks. Phase-delays can destabilize global synchronizatio…
Phase-based spatial ordinal patterns for characterizing oscillatory dynamics
Robison J. Santos-Silva, Bruno R. R. Boaretto, Thiago L. Prado +1
The emergence of organized spatiotemporal patterns is ubiquitous in oscillatory systems, from neural populations to engineered networks. Identifying these patterns and tracking how…
Delay coordinates synchronization and induces abrupt transition in excitable networks
Bruno R. R. Boaretto, Kalel L. Rossi, Lyle E. Muller +2
Neuronal communication is inherently time-delayed, due to the finite speed of signal propagation. Although often considered challenging or disruptive, such time delays can also end…
Exact expression for maximum Lyapunov exponent during transients in computationally powerful dynamical networks
Arthur S. Powanwe, Luisa H. B. Liboni, Anif N. Shikder +7
We study a network whose rich spatiotemporal dynamics have recently been shown to enable dynamics-based computation, including logic gates, short-term memory, and simple encryption…
An explicit operator explains end-to-end computation in the modern neural networks used for sequence and language modeling
Anif N. Shikder, Ramit Dey, Sayantan Auddy +6
We establish a mathematical correspondence between state space models, a state-of-the-art architecture for capturing long-range dependencies in data, and an exactly solvable nonlin…
Geometric perspective of linear stability in finite networks of nonlinear oscillators
Yashee Sinha, Priya B. Jain, Antonio Mihara +4
We use a complex-valued transformation of the Kuramoto model to develop an operator-description of the linear stability in finite networks of nonlinear oscillators. This mathematic…
Traveling Waves Integrate Spatial Information Through Time
Mozes Jacobs, Roberto C. Budzinski, Lyle Muller +2
Traveling waves of neural activity are widely observed in the brain, but their precise computational function remains unclear. One prominent hypothesis is that they enable the tran…
A mathematical language for linking fine-scale structure in spikes from hundreds to thousands of neurons with behaviour
Alexandra N. Busch, Roberto C. Budzinski, Federico W. Pasini +8
Recent advances in neural recording technology allow simultaneously recording action potentials from hundreds to thousands of neurons in awake, behaving animals. However, character…
Image segmentation with traveling waves in an exactly solvable recurrent neural network
Luisa H. B. Liboni, Roberto C. Budzinski, Alexandra N. Busch +4
We study image segmentation using spatiotemporal dynamics in a recurrent neural network where the state of each unit is given by a complex number. We show that this network generat…
An exact mathematical description of computation with transient spatiotemporal dynamics in a complex-valued neural network
Roberto C. Budzinski, Alexandra N. Busch, Samuel Mestern +7
We study a complex-valued neural network (cv-NN) with linear, time-delayed interactions. We report the cv-NN displays sophisticated spatiotemporal dynamics, including partially syn…
Theory of transient chimeras in finite Sakaguchi-Kuramoto networks
Roberto C. Budzinski, James W. C. Graham, Ján Mináč +1
Chimera states are a phenomenon in which order and disorder can co-exist within a network that is fully homogeneous. Precisely how transient chimeras emerge in finite networks of K…
Composed solutions of synchronized patterns in multiplex networks of Kuramoto oscillators
Priya B. Jain, Tung T. Nguyen, Ján Mináč +2
Networks with different levels of interactions, including multilayer and multiplex networks, can display a rich diversity of dynamical behaviors and can be used to model and study…
Dynamical properties and mechanisms of metastability: a perspective in neuroscience
Kalel L. Rossi, Roberto C. Budzinski, Everton S. Medeiros +3
Metastability, characterized by a variability of regimes in time, is a ubiquitous type of neural dynamics. It has been formulated in many different ways in the neuroscience literat…
Broadcasting solutions on networked systems of phase oscillators
Tung T. Nguyen, Roberto C. Budzinski, Federico W. Pasini +3
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…
Small changes at single nodes can shift global network dynamics
Kalel L. Rossi, Roberto C. Budzinski, Bruno R. R. Boaretto +2
Understanding the sensitivity of a system's behavior with respect to parameter changes is essential for many applications. This sensitivity may be desired - for instance in the bra…
Analytical prediction of specific spatiotemporal patterns in nonlinear oscillator networks with distance-dependent time delays
Roberto C. Budzinski, Tung T. Nguyen, Gabriel B. Benigno +4
We introduce an analytical approach that allows predictions and mechanistic insights into the dynamics of nonlinear oscillator networks with heterogeneous time delays. We demonstra…
Equilibria in Kuramoto oscillator networks: An algebraic approach
Tung T. Nguyen, Roberto C. Budzinski, Jacqueline Doan +3
Kuramoto networks constitute a paradigmatic model for the investigation of collective behavior in networked systems. Despite many advances in recent years, many open questions rema…
Geometry unites synchrony, chimeras, and waves in nonlinear oscillator networks
Roberto C. Budzinski, Tung T. Nguyen, Jacqueline Doan +3
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 superconductor…