6 papers
Modules as effective nodes in coarse-grained networks of Kuramoto oscillators
Leonardo L. Bosnardo, Marcus A. M. de Aguiar
Most real-world networks exhibit a significant degree of modularity. Understanding the effects of such topology on dynamical processes is pivotal for advances in social and natural…
Arnold tongues in the forced Kuramoto model with matrix coupling
Guilherme S. Costa, Marcus A. M. de Aguiar
We consider a generalization of the Kuramoto model in which phase oscillators are represented by unit vectors coupled by a matrix of constant coefficients. We show that, when the o…
Synchronization of identical oscillators on a sphere: exact results with external forces and higher-order interactions
Guilherme S. Costa, Marcel Novaes, Ricardo Fariello +1
We study the dynamics of the Kuramoto model on the sphere under higher-order interactions and an external periodic force. For identical oscillators, we introduce a novel way to inc…
Exact solutions of the Kuramoto model with asymmetric higher order interactions of arbitrary order
Guilherme S. Costa, Marcel Novaes, Marcus A. M. de Aguiar
Higher order interactions can lead to new equilibrium states and bifurcations in systems of coupled oscillators described by the Kuramoto model. However, even in the simplest case…
The transition to speciation in the finite genome Derrida-Higgs model: a heuristic solution
Vitor M. Marquioni, Marcus A. M. de Aguiar
The process of speciation, where an ancestral species divides in two or more new species, involves several geographic, environmental and genetic components that interact in a compl…
Bifurcations in the Kuramoto model with external forcing and higher-order interactions
Guilherme S. Costa, Marcel Novaes, Marcus A. M. de Aguiar
Synchronization is an important phenomenon in a wide variety of systems comprising interacting oscillatory units, whether natural (like neurons, biochemical reactions, cardiac cell…