Edmilson Roque

Author(s): Masanori Hanada, Hidehiko Shimada, and Masaki Tezuka

We propose the existence of a new universality in classical chaotic systems when the number of degrees of freedom is large: the statistical property of the Lyapunov spectrum is described by random matrix theory. We demonstrate it by studying the finite-time Lyapunov exponents of the matrix model of ...

[Phys. Rev. E 97, 022224] Published Wed Feb 28, 2018

Author(s): Yu-Zhong Chen and Ying-Cheng Lai

Revealing the structure and dynamics of complex networked systems from observed data is a problem of current interest. Is it possible to develop a completely data driven framework to decipher the network structure and different types of {\em binary} dynamical processes on complex networks? We develo...

[Phys. Rev. E] Published Wed Feb 28, 2018

In this work we applied several concepts on the modeling of complex systems in an attempt to save mankind in the case of a zombie apocalypse. We developed a dynamical system in order to model a zombie outbreak in which we, regular humans, are aided by military personnel in the fight against the zombies. Our analysis has shown that the initial amount of military personnel play a key rule on our survival, even when the zombies are extremely aggressive and in large advantage.This document is a pre-print version of the paper de Mendon\c{c}a, J.P.A., Teixeira, L.M.V., Sato, F. et al. Math Intelligencer (2019). https://doi.org/10.1007/s00283-019-09893-9.

In this work, we address the problem of identifying sparse continuous-time dynamical systems when the spacing between successive samples (the sampling period) is not constant over time. The proposed approach combines the leave-one-sample-out cross-validation error trick from machine learning with an iterative subset growth method to select the subset of basis functions that governs the dynamics of the system. The least-squares solution using only the selected subset of basis functions is then used. The approach is illustrated on two examples: a 6-node feedback ring and the Van der Pol oscillator.

Author(s): David Darmon

In the absence of mechanistic or phenomenological models of real world systems, data-driven models become necessary. The discovery of various embedding theorems in the 1980s and 1990s motivated a powerful set of tools for analyzing deterministic dynamical systems via delay-coordinate embeddings of o...

[Phys. Rev. E] Published Wed Feb 28, 2018

Studies regarding knowledge organization and acquisition are of great importance to understand areas related to science and technology. A common way to model the relationship between different concepts is through complex networks. In such representations, network's nodes store knowledge and edges represent their relationships. Several studies that considered this type of structure and knowledge acquisition dynamics employed one or more agents to discover node concepts by walking on the network. In this study, we investigate a different type of dynamics considering a single node as the "network brain". Such brain represents a range of real systems such as the information about the environment that is acquired by a person and is stored in the brain. To store the discovered information in a specific node, the agents walk on the network and return to the brain. We propose three different dynamics and test them on several network models and on a real system, which is formed by journal articles and their respective citations. Surprisingly, the results revealed that, according to the adopted walking models, the efficiency of self-knowledge acquisition has only a weak dependency on the topology, search strategy and localization of the network brain.

A pedestrian’s physical movement is simulated as a response to the pedestrian subjective evaluation of the objective environment. The objective environment is modeled by presumed fields statically or dynamically superposed. Regulation functions, which consider not only force caused by presumed fields but also local crowd densities around pedestrians, are introduced for consideration of pedestrians’ intelligence. Numerical experiments indicate that the model can be calibrated to reproduce a fundamental diagram that matches an empirical one proposed by Weidmann. Such experiments prove the model to be a useful tool for study of pedestrian dynamics.

We study the completely synchronized states (CSSs) of a system of coupled logistic maps as a function of three parameters: interaction strength ($\varepsilon$), range of the interaction ($\alpha$), that can vary from first-neighbors to global coupling, and a parameter ($\beta$) that allows to scan continuously from non-delayed to one-time delayed dynamics. % We identify in the plane $\alpha$-$\varepsilon$ periodic orbits, limit cycles and chaotic trajectories, and describe how these structures change with the delay. These features can be explained by studying the bifurcation diagrams of a two-dimensional non-delayed map. This allows us to understand the effects of one-time delays on CSSs, e.g, regularization of chaotic orbits and synchronization of short-range coupled maps, observed when the dynamics is moderately delayed. Finally, we substitute the logistic map by cubic and logarithmic maps, in order to test the robustness of our findings.

We review the occurrence of the patterns of the onset of chaos in low-dimensional nonlinear dissipative systems in leading topics of condensed matter physics and complex systems of various disciplines. We consider the dynamics associated with the attractors at period-doubling accumulation points and at tangent bifurcations to describe features of glassy dynamics, critical fluctuations and localization transitions. We recall that trajectories pertaining to the routes to chaos form families of time series that are readily transformed into networks via the Horizontal Visibility algorithm, and this in turn facilitates establish connections between entropy and Renormalization Group properties. We discretize the replicator equation of game theory to observe the onset of chaos in familiar social dilemmas, and also to mimic the evolution of high-dimensional ecological models. We describe an analytical framework of nonlinear mappings that reproduce rank distributions of large classes of data (including Zipf's law). We extend the discussion to point out a common circumstance of drastic contraction of configuration space driven by the attractors of these mappings. We mention the relation of generalized entropy expressions with the dynamics along and at the period doubling, intermittency and quasi-periodic routes to chaos. Finally, we refer to additional natural phenomena in complex systems where these conditions may manifest.

The rotation number of orientation-preserving circle maps that are not necessarily surjective nor injective is discontinuous. In this paper we characterize the circle maps that are points of discontinuity of the rotation number and the relationship between its various possible values on a discontinuity. In particular, we show that, for each circle map corresponding to a discontinuity of the rotation number, all orbits are periodic after a fixed number of iterates, and the entire range of possible rotation numbers at each discontinuity is finite.

In networks of dynamical systems, there are spaces defined in terms of equalities of cell coordinates which are flow-invariant under any dynamical system that has a form consistent with the given underlying network structure—the network synchrony subspaces. Given a network and one of its synchrony subspaces, any system with a form consistent with the network, restricted to the synchrony subspace, defines a new system which is consistent with a smaller network, called the quotient network of the original network by the synchrony subspace. Moreover, any system associated with the quotient can be interpreted as the restriction to the synchrony subspace of a system associated with the original network. We call the larger network a lift of the smaller network, and a lift can be interpreted as a result of the cellular splitting of the smaller network. In this paper, we address the question of the uniqueness in this lifting process in terms of the networks’ topologies. A lift G ...

Author(s): M. P. Nerem, D. Salmon, S. Aubin, and J. B. Delos

A Hamiltonian system is said to have nontrivial monodromy if its fundamental action-angle loops do not return to their initial topological state at the end of a closed circuit in angular momentum-energy space. This process has been predicted to have consequences which can be seen in dynamical system...

[Phys. Rev. Lett.] Published Tue Feb 20, 2018

We study the synchronization of Kuramoto oscillators on networks where only a fraction of them is subjected to a periodic external force. When all oscillators receive the external drive the system always synchronize with the periodic force if its intensity is sufficiently large. Our goal is to understand the conditions for global synchronization as a function of the fraction of nodes being forced and how these conditions depend on network topology, strength of internal couplings and intensity of external forcing. Numerical simulations show that the force required to synchronize the network with the external drive increases as the inverse of the fraction of forced nodes. However, for a given coupling strength, synchronization does not occur below a critical fraction, no matter how large is the force. Network topology and properties of the forced nodes also affect the critical force for synchronization. We develop analytical calculations for the critical force for synchronization as a function of the fraction of forced oscillators and for the critical fraction as a function of coupling strength. We also describe the transition from synchronization with the external drive to spontaneous synchronization.

Author(s): M. Tyloo, T. Coletta, and Ph. Jacquod

In network theory, a question of prime importance is how to assess network vulnerability in a fast and reliable manner. With this issue in mind, we investigate the response to external perturbations of coupled dynamical systems on complex networks. We find that for specific, nonaveraged perturbation...

[Phys. Rev. Lett. 120, 084101] Published Thu Feb 22, 2018

Author(s): Liang Cao, Changhai Tian, Zhenhua Wang, Xiyun Zhang, and Zonghua Liu

Explosive synchronization in networked second-order Kuramoto oscillators has been well studied recently and it is revealed that the synchronization process is featured by cluster explosive synchronization. However, little attention has been paid to the influence of noise or perturbation. We here stu...

[Phys. Rev. E 97, 022220] Published Thu Feb 22, 2018

Author(s): Heiko Hoffmann

The general mechanisms behind self-organized criticality (SOC) are still unknown. Several microscopic and mean-field theory approaches have been suggested, but they do not explain the dependence of the exponents on the underlying network topology of the SOC system. Here, we first report the phenomen...

[Phys. Rev. E 97, 022313] Published Thu Feb 22, 2018

In network theory, a question of prime importance is how to assess network vulnerability in a fast and reliable manner. With this issue in mind, we investigate the response to parameter changes of coupled dynamical systems on complex networks. We find that for specific, non-averaged perturbations, the response of synchronous states critically depends on the overlap between the perturbation vector and the eigenmodes of the stability matrix of the unperturbed dynamics. Once averaged over properly defined ensembles of such perturbations, the response is given by new graph topological indices, which we introduce as generalized Kirchhoff indices. These findings allow for a fast and reliable method for assessing the specific or average vulnerability of a network against changing operational conditions, faults or external attacks.

Author(s): Dáibhid Ó Maoiléidigh

To ensure their sensitivity to weak periodic signals, some physical systems likely operate near a Hopf bifurcation. Many systems operating near such a bifurcation exhibit stochastic resonance, but it is unclear which mechanisms for resonance are inherent to the bifurcation. To address this question,...

[Phys. Rev. E] Published Tue Feb 20, 2018

We introduce a family of unsupervised, domain-free, and (asymptotically) model-independent algorithms based on the principles of algorithmic information theory designed to minimize the loss of algorithmic information. The method coarse-grains data in an algorithmic fashion by collapsing regions that can be procedurally regenerated from the compressed version. We show that the method can preserve the salient properties of objects and structures in the process of data dimension reduction and denoising. Using suboptimal approximations of efficient (polynomial) estimations to algorithmic complexity by recent numerical methods of algorithmic probability we demonstrate how these algorithms can preserve structure properties, outperforming other algorithms in e.g. the area of network dimension reduction. As a case study, we report that the method preserves all the graph-theoretic indices measured on a well-known set of synthetic and real-world networks of very different nature, ranging from degree distribution and clustering coefficient to edge betweenness and degree and eigenvector centralities, achieving equal or significantly better results than other data reduction and some of the leading network sparsification methods.

We consider the long-time dynamics of a general class of nonlinear Fokker-Planck equations, describing the large population behavior of mean-field interacting units. The main motivation of this work concerns the case where the individual dynamics is excitable, i.e. when each isolated dynamics rests in a stable state, whereas a sufficiently strong perturbation induces a large excursion in the phase space. We address the question of the emergence of oscillatory behaviors induced by noise and interaction in such systems. We tackle this problem by considering this model as a slow-fast system (the mean value of the process giving the slow dynamics) in the regime of small individual dynamics and by proving the existence of a positively stable invariant manifold, whose slow dynamics is at first order the dynamics of a single individual averaged with a Gaussian kernel. We consider applications of this result to Stuart-Landau, FitzHugh-Nagumo and Cucker-Smale oscillators.

In skew-product systems with contractive factors, all orbits asymptotically approach the graph of the so-called sync function; hence, the corresponding regularity properties primarily matter. In the literature, sync function Lipschitz continuity and differentiability have been proved to hold depending on the derivative of the base reciprocal, if not on its Lyapunov exponent. However, forcing topological features can also impact the sync function regularity. Here, we estimate the total variation of sync functions generated by one-dimensional Markov maps. A sharp condition for bounded variation is obtained depending on parameters, that involves the Markov map topological entropy. The results are illustrated with examples.

We have compared the phase synchronization transition of the second order Kuramoto model on 2D lattices and on large, synthetic power-grid networks, generated from real data. The latter are weighted, hierarchical modular networks. Due to the inertia the synchronization transitions are of first order type, characterized by fast relaxation and hysteresis by varying the global coupling parameter $K$. Finite size scaling analysis shows that there is no real phase transition in the thermodynamic limit, unlike in the mean-field model. The order parameter and its fluctuations do not depend on the network size. In case of the power-grids the phase synchronization is weaker and breaks down at a higher $K$, than in case of lattices. The temporal behavior of de-synchronization avalanches has been followed and duration distributions with power-law tails have been detected below the transition in case of quenched, intrinsic frequencies of the nodes. This suggests rare region effects, resulting in scale-free distributions even without a self organization mechanism.

Dynamical complexity and computation in recurrent neural networks beyond their fixed point

Dynamical complexity and computation in recurrent neural networks beyond their fixed point, Published online: 20 February 2018; doi:10.1038/s41598-018-21624-2

Dynamical complexity and computation in recurrent neural networks beyond their fixed point

We seek to infer the parameters of an ergodic Markov process from samples taken independently from the steady state. Our focus is on non-equilibrium processes, where the steady state is not described by the Boltzmann measure, but is generally unknown and hard to compute, which prevents the application of established equilibrium inference methods. We propose a quantity we call propagator likelihood, which takes on the role of the likelihood in equilibrium processes. This propagator likelihood is based on fictitious transitions between those configurations of the system which occur in the samples. The propagator likelihood can be derived by minimising the relative entropy between the empirical distribution and a distribution generated by propagating the empirical distribution forward in time. Maximising the propagator likelihood leads to an efficient reconstruction of the parameters of the underlying model in different systems, both with discrete configurations and with continuous...

Author(s): Dominique Chu

A central result of stochastic thermodynamics is that irreversible state transitions of Markovian systems entail a cost in terms of an infinite entropy production. A corollary of this is that strictly deterministic computation is not possible. Using a thermodynamically consistent model, we show that...

[Phys. Rev. E 97, 022121] Published Thu Feb 15, 2018

Author(s): Liang Cao, Changhai Tian, Zhenhua Wang, Xiyun Zhang, and Zonghua Liu

Explosive synchronization in networked second-order Kuramoto oscillators has been well studied recently and it is revealed that the synchronization process is featured by cluster explosive synchronization. However, little attention has been paid to the influence of noise or perturbation. We here stu...

[Phys. Rev. E] Published Mon Feb 12, 2018

Author(s): Jinha Park and B. Kahng

The Kuramoto model with mixed signs of couplings is known to produce a traveling-wave synchronized state. Here, we consider an abrupt synchronization transition from the incoherent state to the traveling-wave state through a long-lasting metastable state with large fluctuations. Our explanation of t...

[Phys. Rev. E] Published Tue Feb 13, 2018

Author(s): Heiko Hoffmann

The general mechanisms behind self-organized criticality (SOC) are still unknown. Several microscopic and mean-field theory approaches have been suggested, but they do not explain the dependence of the exponents on the underlying network topology of the SOC system. Here, we first report the phenomen...

[Phys. Rev. E] Published Tue Feb 13, 2018

Train PhD students to be thinkers not just specialists

Train PhD students to be thinkers not just specialists, Published online: 14 February 2018; doi:10.1038/d41586-018-01853-1

Many doctoral curricula aim to produce narrowly focused researchers rather than critical thinkers. That can and must change, says Gundula Bosch.

Author(s): Filippo Radicchi

According to a recent information-theoretical proposal, the problem of defining and identifying communities in networks can be interpreted as a classical communication task over a noisy channel: memberships of nodes are information bits erased by the channel, edges and non-edges in the network are p...

[Phys. Rev. E] Published Tue Feb 13, 2018