34 results found
Nijholt E, Ocampo-Espindola JL, Eroglu D, et al., 2022, Emergent hypernetworks in weakly coupled oscillators., Nat Commun, Vol: 13
Networks of weakly coupled oscillators had a profound impact on our understanding of complex systems. Studies on model reconstruction from data have shown prevalent contributions from hypernetworks with triplet and higher interactions among oscillators, in spite that such models were originally defined as oscillator networks with pairwise interactions. Here, we show that hypernetworks can spontaneously emerge even in the presence of pairwise albeit nonlinear coupling given certain triplet frequency resonance conditions. The results are demonstrated in experiments with electrochemical oscillators and in simulations with integrate-and-fire neurons. By developing a comprehensive theory, we uncover the mechanism for emergent hypernetworks by identifying appearing and forbidden frequency resonant conditions. Furthermore, it is shown that microscopic linear (difference) coupling among units results in coupled mean fields, which have sufficient nonlinearity to facilitate hypernetworks. Our findings shed light on the apparent abundance of hypernetworks and provide a constructive way to predict and engineer their emergence.
Poignard C, Pade JP, Pereira T, 2019, The effects of structural perturbations on the synchronizability of diffusive networks, Journal of Nonlinear Science, Vol: 29, Pages: 1919-1942, ISSN: 0938-8974
We investigate the effects of structural perturbations on the networks ability to synchronize. We establish a classification of directed links according to their impact on synchronizability. We focus on adding directed links in weakly connected networks having a strongly connected component acting as driver. When the connectivity of the driver is not stronger than the connectivity of the slave component, we can always make the network strongly connected while hindering synchronization. On the other hand, we prove the existence of a perturbation which makes the network strongly connected while increasing the synchronizability. Under additional conditions, there is a node in the driving component such that adding a single link starting at an arbitrary node of the driven component and ending at this node increases the synchronizability.
Poignard C, Pereira T, Pade JP, 2018, SPECTRA OF LAPLACIAN MATRICES OF WEIGHTED GRAPHS: STRUCTURAL GENERICITY PROPERTIES, SIAM JOURNAL ON APPLIED MATHEMATICS, Vol: 78, Pages: 372-394, ISSN: 0036-1399
Stankovski T, Pereira T, McClintock PVE, et al., 2017, Coupling functions: Universal insights into dynamical interaction mechanisms, REVIEWS OF MODERN PHYSICS, Vol: 89, ISSN: 0034-6861
Vlasov V, Zou Y, Pereira T, 2015, Explosive synchronization is discontinuous, PHYSICAL REVIEW E, Vol: 92, ISSN: 1539-3755
Zou Y, Pereira T, Small M, et al., 2014, Basin of Attraction Determines Hysteresis in Explosive Synchronization, PHYSICAL REVIEW LETTERS, Vol: 112, ISSN: 0031-9007
Pereira T, Eldering J, Rasmussen M, et al., 2014, Towards a theory for diffusive coupling functions allowing persistent synchronization, Nonlinearity, Vol: 27, Pages: 501-525, ISSN: 0951-7715
Pereira T, van Strien S, Lamb JSW, 2013, Dynamics of Coupled Maps in Heterogeneous Random Networks
We study the emergence of coherence in complex networks of mutually coupled nonidentical elements. We uncover the precise dependence of the dynamical coherence on the network connectivity, the isolated dynamics of the elements, and the coupling function. These findings predict that in random graphs the enhancement of coherence is proportional to the mean degree. In locally connected networks, coherence is no longer controlled by the mean degree but rather by how the mean degree scales with the network size. In these networks, even when the coherence is absent, adding a fraction s of random connections leads to an enhancement of coherence proportional to s. Our results provide a way to control the emergent properties by the manipulation of the dynamics of the elements and the network connectivity.
Florence G, Pereira T, Kurths J, 2012, Extracellular potassium dynamics in the hyperexcitable state of the neuronal ictal activity, Communications in Nonlinear Science and Numerical Simulation, Vol: 17, Pages: 4700-4706, ISSN: 1007-5704
Batista CAS, Lameu EL, Batista AM, et al., 2012, Phase synchronization of bursting neurons in clustered small-world networks, PHYSICAL REVIEW E, Vol: 86, ISSN: 1539-3755
Veneziani AM, Pereira T, Marchetti DHU, 2012, Asymptotic integral kernel for ensembles of random normal matrices with radial potentials, Journal of Mathematical Physics, Vol: 53, ISSN: 0022-2488
Veneziani AM, Pereira T, Marchetti DHU, 2011, Conformal deformation of equilibrium measures in normal random ensembles, Journal of Physics A: Mathematical and Theoretical, Vol: 44, ISSN: 1751-8113
Pereira T, 2010, Hub synchronization in scale-free networks, PHYSICAL REVIEW E, Vol: 82, ISSN: 2470-0045
Pereira T, Marchetti DHU, 2009, Quantum States Allowing Minimum Uncertainty Product of and Lz, Progress of Theoretical Physics, Vol: 122, Pages: 1137-1149, ISSN: 0033-068X
Pereira T, Baptista MS, Reyes MB, et al., 2009, A scenario for torus T2 destruction via a global bifurcation, Chaos, Solitons & Fractals, Vol: 39, Pages: 2198-2210, ISSN: 0960-0779
Pereira T, Thiel M, Baptista MS, et al., 2008, Network mutual information and synchronization under time transformations, NEW JOURNAL OF PHYSICS, Vol: 10, ISSN: 1367-2630
Pereira T, Baptista MS, Kurths J, et al., 2007, Onset of phase synchronization in neurons with chemical synapse, INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, Vol: 17, Pages: 3545-3549, ISSN: 0218-1274
Pereira T, Baptista MS, Kurths J, 2007, Multi-time-scale synchronization and information processing in bursting neuron networks, The European Physical Journal Special Topics, Vol: 146, Pages: 155-168, ISSN: 1951-6355
Pereira T, Baptista MS, Kurths J, 2007, Phase and average period of chaotic oscillators, PHYSICS LETTERS A, Vol: 362, Pages: 159-165, ISSN: 0375-9601
Pereira T, Baptista MS, Kurths J, 2007, General framework for phase synchronization through localized sets, PHYSICAL REVIEW E, Vol: 75, ISSN: 1539-3755
Pereira T, Baptista MS, Kurths J, 2007, Detecting phase synchronization by localized maps: Application to neural networks, EPL, Vol: 77, ISSN: 0295-5075
Baptista MS, Pereira T, Kurths J, 2006, Upper bounds in phase synchronous weak coherent chaotic attractors, PHYSICA D-NONLINEAR PHENOMENA, Vol: 216, Pages: 260-268, ISSN: 0167-2789
Pereira T, Baptista MS, Reyes MB, et al., 2006, Global bifurcation destroying the experimental torus<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>T</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math>, Physical Review E, Vol: 73, ISSN: 1539-3755
Baptista MS, Pereira T, Sartorelli JC, et al., 2004, Phase synchronization and invariant measures in sinusoidally perturbed chaotic systems, EXPERIMENTAL CHAOS, Vol: 742, Pages: 325-329, ISSN: 0094-243X
Baptista MS, Silva TP, Sartorelli JC, et al., 2003, Phase synchronization in the perturbed Chua circuit, Physical Review E, Vol: 67, ISSN: 1063-651X
Veneziani AM, Pereira T, Marchetti DHU, Conformal Deformation from Normal to Hermitian Random Matrix Ensembles
We investigate the eigenvalues statistics of ensembles of normal randommatrices when their order N tends to infinite. In the model the eigenvalueshave uniform density within a region determined by a simple analytic polynomialcurve. We study the conformal deformations of normal random ensembles toHermitian random ensembles and give sufficient conditions for the latter to bea Wigner ensemble.
Batista CAS, Nunes RV, Batista AM, et al., Global synchronization of bursting neurons in clustered networks
We investigate the collective dynamics of bursting neurons on clusterednetwork. The clustered network is composed of subnetworks each presenting asmall-world property, and in a given subnetwork each neuron has a probabilityto be connected to the other subnetworks. We give bounds for the criticalcoupling strength to obtain global burst synchronization in terms of thenetwork structure, i.e., intracluster and intercluster probabilitiesconnections. As the heterogeneity in the network is reduced the network globalsynchronization is improved. We show that the transitions to global synchronymay be abrupt or smooth depending on the intercluster probability.
Veneziani AM, Pereira T, Marchetti DHU, Conformal Universality in Normal Matrix Ensembles
A remarkable property of Hermitian ensembles is their universal behavior,that is, once properly rescaled the eigenvalue statistics does not depend onparticularities of the ensemble. Recently, normal matrix ensembles haveattracted increasing attention, however, questions on universality for theseensembles still remain under debate. We analyze the universality properties ofrandom normal ensembles. We show that the concept of universality used forHermitian ensembles cannot be directly extrapolated to normal ensembles.Moreover, we show that the eigenvalue statistics of random normal matrices withradially symmetric potential can be made universal under a conformaltransformation.
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