arXiv subjects

Sergio R. Lopes

Publications and source records attributed to Sergio R. Lopes.

8 recordsLinked to original sources

arXiv2026

Impact of Channel Dynamics on Higher-order Interactions of Oscillators

Modeling higher-order interactions (HOIs) in nonlinear networks with static topologies is often physically restrictive. We demonstrate that standard 3-body Kuramoto couplings are mathematically equivalent to pairwise connections modulated by latent variables of transmission channels. While standard HOI topologies emerge in the adiabatic limit of these variables, relaxing this constraint reveals that latent channel timescales dictate collective macroscopic states. Specifically, transmission inertia drives bistability for symmetric interaction tensors and anti-phase cluster synchronization for antisymmetric ones. Furthermore, dynamically induced clustering in global topologies emerges as a finite-size effect of the dynamics of the local channels. Ultimately, we show that relying exclusively on static topologies restricts interaction modeling. Integrating latent variables captures the transient inertia and fundamental asymmetry of physical networks, bridging the analytical utility of higher-order functions with the reality of the underlying transmission medium.

nlin.AO↗

arXiv2025

Beat Frequency Induced Transitions in Synchronization Dynamics

In neurosciences, the brain processes information via the firing patterns of connected neurons operating across a spectrum of frequencies. To better understand the effects of these frequencies in the neuron dynamics, we have simulated a neuronal network of Izhikevich neurons to examine the interaction between frequency allocation and intermittent phase synchronization dynamics. As the synchronized population of neurons passes through a bifurcation, an additional frequency mode emerges, enabling a match in the mean frequency while retaining distinct most probable frequencies among neurons. Subsequently, the network intermittently transits between two patterns, one partially synchronized and the other unsynchronized. Through our analysis, we demonstrate that the frequency changes on the network lead to characteristic transition times between synchronization states. Moreover, these transitions adhere to beat frequency statistics when the neurons' frequencies differ by multiples of a frequency gap. Finally, our results can improve the performance in predicting transitions on problems where the beat frequency strongly influences the dynamics.

q-bio.NC↗

arXiv2012

Anomalous transport induced by nonhyperbolicity

In this letter we study how deterministic features presented by a system can be used to perform direct transport in a {\it quasi}-symmetric potential and weak dissipative system. We show that the presence of nonhyperbolic regions around acceleration areas of the phase space plays an important role in the acceleration of particles giving rise to direct transport in the system. Such effect can be observed for a large interval of the weak asymmetric potential parameter allowing the possibility to obtain useful work from unbiased nonequilibrium fluctuation in real systems even in a presence of a {\it quasi}-symmetric potential.

nlin.CD↗

arXiv2010

Parametric evolution of unstable dimension variability in coupled piecewise-linear chaotic maps

In presence of unstable dimension variability numerical solutions of chaotic systems are valid only for short periods of observation. For this reason, analytical results for systems that exhibit this phenomenon are needed. Aiming to go one step further in obtaining such results, we study the parametric evolution of unstable dimension variability in two coupled bungalow maps. Each of these maps presents intervals of linearity that define Markov partitions, which are recovered for the coupled system in the case of synchronization. Using such partitions we find exact results for the onset of unstable dimension variability and for contrast measure, which quantifies the intensity of the phenomenon in terms of the stability of the periodic orbits embedded in the synchronization subspace.

nlin.CD↗

arXiv2009

Periodic orbit analysis at the onset of the unstable dimension variability and at the blowout bifurcation

Many chaotic dynamical systems of physical interest present a strong form of nonhyperbolicity called unstable dimension variability (UDV), for which the chaotic invariant set contains periodic orbits possessing different numbers of unstable eigendirections. The onset of UDV is usually related to the loss of transversal stability of an unstable fixed point embedded in the chaotic set. In this paper, we present a new mechanism for the onset of UDV, whereby the period of the unstable orbits losing transversal stability tends to infinity as we approach the onset of UDV. This mechanism is unveiled by means of a periodic orbit analysis of the invariant chaotic attractor for two model dynamical systems with phase spaces of low dimensionality, and seems to depend heavily on the chaotic dynamics in the invariant set. We also described, for these systems, the blowout bifurcation (for which the chaotic set as a whole loses transversal stability) and its relation with the situation where the effects of UDV are the most intense. For the latter point, we found that chaotic trajectories off, but very close to, the invariant set exhibit the same scaling characteristic of the so-called on-off intermittency.

nlin.CD↗

arXiv2009

Periodic-orbit analysis and scaling laws of intermingled basins of attraction in an ecological dynamical system

Chaotic dynamical systems with two or more attractors lying on invariant subspaces may, provided certain mathematical conditions are fulfilled, exhibit intermingled basins of attraction: Each basin is riddled with holes belonging to basins of the other attractors. In order to investigate the occurrence of such phenomenon in dynamical systems of ecological interest (two-species competition with extinction) we have characterized quantitatively the intermingled basins using periodic-orbit theory and scaling laws. The latter results agree with a theoretical prediction from a stochastic model, and also with an exact result for the scaling exponent we derived for the specific class of models investigated. We discuss the consequences of the scaling laws in terms of the predictability of a final state (extinction of either species) in an ecological experiment.

nlin.CD↗

arXiv2009

Riddling and chaotic synchronization of coupled piecewise-linear Lorenz maps

We investigate the parametric evolution of riddled basins related to synchronization of chaos in two coupled piecewise-linear Lorenz maps. Riddling means that the basin of the synchronized attractor is shown to be riddled with holes belonging to another basin in an arbitrarily fine scale, which has serious consequences on the predictability of the final state for such a coupled system. We found that there are wide parameter intervals for which two piecewise-linear Lorenz maps exhibit riddled basins (globally or locally), which indicates that there are riddled basins in coupled Lorenz equations, as previously suggested by numerical experiments. The use of piecewise-linear maps makes it possible to prove rigorously the mathematical requirements for the existence of riddled basins.

nlin.CD↗

arXiv1996

Nonintegrable Interaction of Ion-Acoustic and Electromagnetic Waves in a Plasma

In this paper we re-examine the one-dimensional interaction of electromagnetic and ion acoustic waves in a plasma. Our model is similar to one solved by Rao et al. (Phys. Fluids, vol. 26, 2488 (1983)) under a number of analytical approximations. Here we perform a numerical investigation to examine the stability of the model. We find that for slightly over dense plasmas, the propagation of stable solitary modes can occur in an adiabatic regime where the ion acoustic electric field potential is enslaved to the electromagnetic field of a laser. But if the laser intensity or plasma density increases or the laser frequency decreases, the adiabatic regime loses stability via a transition to chaos. New asymptotic states are attained when the adiabatic regime no longer exists. In these new states, the plasma becomes rarefied, and the laser field tends to behave like a vacuum field.

chao-dyn↗