41 research outputs found
Perfect synchronization in networks of phase-frustrated oscillators
Synchronizing phase frustrated Kuramoto oscillators, a challenge that has
found applications from neuronal networks to the power grid, is an eluding
problem, as even small phase-lags cause the oscillators to avoid
synchronization. Here we show, constructively, how to strategically select the
optimal frequency set, capturing the natural frequencies of all oscillators,
for a given network and phase-lags, that will ensure perfect synchronization.
We find that high levels of synchronization are sustained in the vicinity of
the optimal set, allowing for some level of deviation in the frequencies
without significant degradation of synchronization. Demonstrating our results
on first and second order phase-frustrated Kuramoto dynamics, we implement them
on both model and real power grid networks, showing how to achieve
synchronization in a phase frustrated environment.Comment: To appear in Europhysics Letters, 7 pages, supplementary informatio
Controlling species densities in structurally perturbed intransitive cycles with higher-order interactions
The persistence of biodiversity of species is a challenging proposition in
ecological communities in the face of Darwinian selection. The present article
investigates beyond the pairwise competitive interactions and provides a novel
perspective for understanding the influence of higher-order interactions on the
evolution of social phenotypes. Our simple model yields a prosperous outlook to
demonstrate the impact of perturbations on intransitive competitive
higher-order interactions. Using a mathematical technique, we show how alone
the perturbed interaction network can quickly determine the coexistence
equilibrium of competing species instead of solving a large system of ordinary
differential equations. It is possible to split the system into multiple
feasible cluster states depending on the number of perturbations. Our analysis
also reveals the ratio between the unperturbed and perturbed species is
inversely proportional to the amount of employed perturbation. Our results
suggest that nonlinear dynamical systems and interaction topologies can be
interplayed to comprehend species' coexistence under adverse conditions.
Particularly our findings signify that less competition between two species
increases their abundance and outperforms others.Comment: 17 pages, 10 figure
Interlayer antisynchronization in degree-biased duplex networks
With synchronization being one of nature's most ubiquitous collective
behaviors, the field of network synchronization has experienced tremendous
growth, leading to significant theoretical developments. However, most of these
previous studies consider uniform connection weights and undirected networks
with positive coupling. In the present article, we incorporate the asymmetry in
a two-layer multiplex network by assigning the ratio of the adjacent nodes'
degrees as the weights to the intralayer edges. Despite the presence of
degree-biased weighting mechanism and attractive-repulsive coupling strengths,
we are able to find the necessary conditions for intralayer synchronization and
interlayer antisynchronization and test whether these two macroscopic states
can withstand demultiplexing in a network. During the occurrence of these two
states, we analytically calculate the oscillator's amplitude. In addition to
deriving the local stability conditions for interlayer antisynchronization via
the master stability function approach, we also construct a suitable Lyapunov
function to determine a sufficient condition for global stability. We provide
numerical evidence to show the necessity of negative interlayer coupling
strength for the occurrence of antisynchronization, and such repulsive
interlayer coupling coefficients can not destroy intralayer synchronization.Comment: 16 pages, 5 figures (Accepted for publication in the journal Physical
Review E