arXiv subjects

Everton S. Medeiros

Publications and source records attributed to Everton S. Medeiros.

17 recordsLinked to original sources

arXiv2026

Dispersal-induced survival of predators in metacommunities due to transient chaos

Dispersal networks critically shape the fate of ecological communities, yet the mechanisms linking connectivity and persistence remain poorly understood. We show that an interplay between asymmetric dispersal and asynchronous dynamics across patches in a dispersal network can prevent predator extinction across broad dispersal ranges, even in identical environments in which synchrony usually drives ecosystems to collapse. Unlike classical rescue effects based on environmental heterogeneity or equilibrium states, this mechanism emerges from non-equilibrium dynamics, specifically from transient chaotic dynamics. Dispersal coupling perturbs local trajectories in patches facing extinction and reinforce chaotic motion, thereby sustaining chaotic oscillations indefinitely. Strikingly, only minimal connectivity is required: small-world networks with a few long-range links suffice to rescue predator populations. These findings reveal a counterintuitive principle that limited, well-placed connectivity can harness chaos to maintain biodiversity in fragmented landscapes.

nlin.CD↗

arXiv2026

Dynamic link switching induces stable synchronized states in sparse networks

The flow of information in networked systems composed of multiple interacting elements strongly depends on the level of connectivity among these elements. Sparse connectivity often hinders the emergence of states in which information is globally shared, such as fully synchronized states. In this context, dynamically switching existing network links among system elements can facilitate the onset of synchronization. Here, we address this problem in a double-layer network of FitzHugh-Nagumo oscillators with sparse inter-layer connectivity at fixed density. We show that dynamically switching the existing cross-layer links induces inter-layer synchronization, with a clear dependence on the switching time. In agreement with intuition, shorter switching times suppress large deviations between temporally connected oscillators and more effectively promote synchronization; crucially, this effect persists even when each isolated layer is chaotic. Chaos at the layer level is verified by a strictly positive largest Lyapunov exponent, confirming that synchrony is induced by switching rather than by periodic dynamics. For a minimal double-layer system, we emulate switching using smooth square waves and compute the master stability function (MSF), which is in agreement with direct numerical simulations and delineates the stability regions in parameter space.

nlin.AO↗

arXiv2025

Breakdown of stochastic resonance in complex networks

In networked systems, stochastic resonance occurs as a collective phenomenon where the entire stochastic network resonates with a weak applied periodic signal. Beyond the interplay among the network coupling, the amplitude of the external periodic signal, and the intensity of stochastic fluctuations, the maintenance of stochastic resonance also crucially depends on the resonance capacity of each oscillator composing the network. This scenario raises the question: Can local defects in the ability of oscillators to resonate break down the stochastic resonance phenomenon in the entire network? Here, we investigate this possibility in complex networks of prototypical bistable oscillators in a double-well potential. We test the sustainability of stochastic resonance by considering a fraction of network oscillators with nonresonant potential landscapes. We find that the number of nonresonant oscillators depends nonlinearly on their dissimilarity from the rest of the network oscillators. In addition, we unravel the role of the network topology and coupling strength in maintaining, or suppressing, the stochastic resonance for different noise levels and number of nonresonant oscillators. Finally, we obtain a low-dimensional deterministic model confirming the results observed for the networks.

nlin.AO↗

arXiv2024

Transients versus network interactions give rise to multistability through trapping mechanism

In networked systems, the interplay between the dynamics of individual subsystems and their network interactions has been found to generate multistability in various contexts. Despite its ubiquity, the specific mechanisms and ingredients that give rise to multistability from such interplay remain poorly understood. In a network of coupled excitable units, we show that this interplay generating multistability occurs through a competition between the units' transient dynamics and their coupling. Specifically, the diffusive coupling between the units manages to reinject them in the excitability region of their individual state space and effectively trap them there. We show that this trapping mechanism leads to the coexistence of multiple types of oscillations: periodic, quasiperiodic, and even chaotic, although the units separately do not oscillate. Interestingly, we show that the attractors emerge through different types of bifurcations - in particular, the periodic attractors emerge through either saddle-node of limit cycles bifurcations or homoclinic bifurcations - but in all cases the reinjection mechanism is present.

math.DS↗

arXiv2024

Dynamical properties and mechanisms of metastability: a perspective in neuroscience

Metastability, characterized by a variability of regimes in time, is a ubiquitous type of neural dynamics. It has been formulated in many different ways in the neuroscience literature, however, which may cause some confusion. In this Perspective, we discuss metastability from the point of view of dynamical systems theory. We extract from the literature a very simple but general definition through the concept of metastable regimes as long-lived but transient epochs of activity with unique dynamical properties. This definition serves as an umbrella term that encompasses formulations from other works, and readily connects to concepts from dynamical systems theory. This allows us to examine general dynamical properties of metastable regimes, propose in a didactic manner several dynamics-based mechanisms that generate them, and discuss a theoretical tool to characterize them quantitatively. This perspective leads to insights that help to address issues debated in the literature and also suggest pathways for future research.

q-bio.NC↗

arXiv2024

Local control for the collective dynamics of self-propelled particles

Utilizing a paradigmatic model for the motion of interacting self-propelled particles, we demonstrate that local accelerations at the level of individual particles can drive transitions between different collective dynamics, leading to a control process. We find that the ability to trigger such transitions is hierarchically distributed among the particles and can form distinctive spatial patterns within the collective. Chaotic dynamics occur during the transitions, which can be attributed to fractal basin boundaries mediating the control process. The particle hierarchies described in this study offer decentralized capabilities for controlling artificial swarms.

cond-mat.soft↗

arXiv2024

Singular fractal dimension at periodicity cascades in parameters spaces

In the parameter spaces of nonlinear dynamical systems, we investigate the boundaries between periodicity and chaos and unveil the existence of fractal sets characterized by a singular fractal dimension. This dimension stands out from the typical fractal dimensions previously considered universal for these parameter boundaries. We show that the singular fractal sets dwell along parameter curves, called extreme curves, that intersect periodicity cascades at their center of stability in all scales of parameters spaces. The results reported here are generally demonstrated for the class of one-dimensional maps with at least two control parameters, generalizations to other classes of systems are possible.

nlin.CD↗

arXiv2023

Scale-free avalanches in arrays of FitzHugh-Nagumo oscillators

The activity in the brain cortex remarkably shows a simultaneous presence of robust collective oscillations and neuronal avalanches, where intermittent bursts of pseudo-synchronous spiking are interspersed with long periods of quiescence. The mechanisms allowing for such a coexistence are still a matter of an intensive debate. Here, we demonstrate that avalanche activity patterns can emerge in a rather simple model of an array of diffusively coupled neural oscillators with multiple timescale local dynamics in vicinity of a canard transition. The avalanches coexist with the fully synchronous state where the units perform relaxation oscillations. We show that the mechanism behind the avalanches is based on an inhibitory effect of interactions, which may quench the spiking of units due to an interplay with the maximal canard. The avalanche activity bears certain heralds of criticality, including scale-invariant distributions of event sizes. Furthermore, the system shows an increased sensitivity to perturbations, manifested as critical slowing down and a reduced resilience.

nlin.AO↗

arXiv2023

Chimera states emerging from dynamical trapping in chaotic saddles

Nonlinear systems possessing nonattracting chaotic sets, such as chaotic saddles, embedded in their state space may oscillate chaotically for a transient time before eventually transitioning into some stable attractor. We show that these systems, when networked with nonlocal coupling in a ring, are capable of forming chimera states, in which one subset of the units oscillates periodically in a synchronized state forming the coherent domain, while the complementary subset oscillates chaotically in the neighborhood of the chaotic saddle constituting the incoherent domain. We find two distinct transient chimera states distinguished by their abrupt or gradual termination. We analyze the lifetime of both chimera states, unraveling their dependence on coupling range and size. We find an optimal value for the coupling range yielding the longest lifetime for the chimera states. Moreover, we implement transversal stability analysis to demonstrate that the synchronized state is asymptotically stable for network configurations studied here.

nlin.CD↗

arXiv2022

Solitary states in complex networks: impact of topology

The dynamical behavior of networked systems is expected to reflect the features of their coupling structure. Yet, symmetry-broken solutions often occur in symmetrically coupled networks. An example is provided by the so-called solitary states where the dynamics of one network node is different from the entire symmetric network. Here, we investigate the structural constraints of networks for the appearance of solitary states in their dynamics. By performing a large number of numerical simulations, we find that such states occur with high probability in asymmetric networks, such as the ones exhibiting the scale-free property. Next, we analyze the structural features of the networks demonstrating solitary states to reveal that the minimum number of connections in the adjacent nodes of a solitary one is crucial for the appearance of the solitary states. Finally, we perform bifurcation analysis of a dimension-reduced system, confirming the influence of the connectivity of the neighboring nodes on the solitary ones.

nlin.PS↗

arXiv2021

Coupling-induced periodic windows in networked discrete-time systems

Networked nonlinear systems present a variety of emergent phenomena as a result of the mutual interactions between their units. An interesting feature of these systems is the presence of stable periodic behavior even when each unit oscillates chaotically if in isolation. Surprisingly, the mechanism in which the network interaction replaces chaos by periodicity is still poorly understood. Here, we show that such an onset of regularity can occur via replication of periodic windows. This phenomenon multiplies the stability domains in the system parameter space, not only suppressing chaos but also making the network less vulnerable to external disturbances such as shocks and noise. Moreover, we observe that the network cluster synchronizes for the parameters corresponding to the replica periodic windows. To confirm these observations, we employ the formalism of the master stability function demonstrating that the complete synchronized state is indeed transversally unstable in the replica windows.

nlin.AO↗

arXiv2021

Sparsity-driven synchronization in oscillators networks

The emergence of synchronized behavior is a direct consequence of networking dynamical systems. Naturally, strict instances of this phenomenon, such as the states of complete synchronization are favored, or even ensured, in networks with a high density of connections. Conversely, in sparse networks, the system state-space is often shared by a variety of coexistent solutions. Consequently, the convergence to complete synchronized states is far from being certain. In this scenario, we report the surprising phenomenon in which completely synchronized states are made the sole attractor of sparse networks by removing network links, the sparsity-driven synchronization. This phenomenon is observed numerically for nonlocally coupled Kuramoto networks and verified analytically for locally coupled ones. In addition, we reduce the network equations to a one-dimension dynamical system to unravel the bifurcation scenario underlying the network transition to completely synchronized behavior. Furthermore, we present a simple procedure, based on the bifurcations in the thermodynamic limit, that determines the minimum number of links to be removed in order to ensure complete synchronization. Finally, we propose an application of the reported phenomenon as a control scheme to drive complete synchronization in high connectivity networks.

nlin.AO↗

arXiv2021

Edges of inter-layer synchronization in multilayer networks with time-switching links

We investigate the transition to synchronization in a two-layer network with time-switching inter-layer links. We focus on the role of the number of inter-layer links and the time-scale of topological changes. Initially, we observe a smooth transition to complete synchronization for the static inter-layer topology by increasing the number of inter-layer links. Next, for a dynamic topology with the existent inter-layer links randomly changing among identical units in the layers, we observe a significant improvement in the system synchronizability, i.e., the layers synchronize with lower inter-layer connectivity. More interestingly, we find that, for a critical switching-time, the transition to synchronization occurs abruptly as the number of inter-layer links increases. We interpret this phenomenon as the shrinking, and ultimately, the disappearance of the basin of attraction of a desynchronized network state.

nlin.AO↗

arXiv2020

Solitary states in multiplex neural networks: onset and vulnerability

We investigate solitary states in a two-layer multiplex network of FitzHugh-Nagumo neurons in the oscillatory regime. We demonstrate how solitary states can be induced in a multiplex network consisting of two non-identical layers. More specifically, we show that these patterns can be introduced via weak multiplexing into a network that is fully synchronized in isolation. We show that this result is robust under variations of the inter-layer coupling strength and largely independent of the choice of initial conditions. Moreover, we study the vulnerability of solitary states with respect to changes in the inter-layer topology. In more detail, we remove links that connect two solitary nodes of each layer and evaluate the resulting pattern. We find a highly non-trivial dependence of the survivability of the solitary states on topological (position in the network) and dynamical (phase of the oscillation) characteristics.

nlin.AO↗

arXiv2020

Geomagnetic reversals at the edge of regularity

Geomagnetic field reversals remain as one of the most intriguing problems in geophysics and are regarded as chaotic processes resulting from a dynamo mechanism. In this article, we use the polarity scale data set for the last 170 Myr from the ocean's floor to provide robust evidence for an inverse relationship between the complexity of sequences of consecutive polarity intervals and the respective reversal rate. In particular the variability of sequences of polarity intervals reaches a minimum in the mid-Jurassic when a maximum reversal rate is found. This raises the possibility of epochs of high regularity in the reversal process geodynamo. To shed light on this process, We investigate the transition from regular to chaotic regime in a minimal model for geomagnetic reversals. We show that even in a chaotic regime, near to the transition the system retains the signature of regular behavior. We suggest that geomagnetic reversals have switched between different degrees of irregularity, with a dominant periodicity around 70 kyrs that results from a "ghost" limit cycle.

physics.geo-ph↗

arXiv2019

Evidence for crisis-induced intermittency during geomagnetic superchron transitions

The geomagnetic field's dipole undergoes polarity reversals in irregular time intervals. Particularly long periods (of the order of $10^7$yrs) without reversals, named superchrons, have occurred at least three times in history. We provide observational evidence for high non-Gaussianity in the vicinity of a transition to and from a geomagnetic superchron, consisting of a sharp increase in high-order moments (skewness and kurtosis) of the dipole's distribution. Such increase in the moments is a universal feature of crisis-induced intermittency in low-dimensional dynamical systems undergoing global bifurcations. This suggests temporal variation of the underlying parameters of the physical system. Through a low dimensional system that models the geomagnetic reversals we show that the increase in the high-order moments during transitions to geomagnetic superchrons is caused by the progressive destruction of global periodic orbits exhibiting both polarities as the system approaches a merging bifurcation. We argue that the non-gaussianity in this system is caused by the redistribution of the attractor around local cycles as global ones are destroyed.

physics.geo-ph↗

arXiv2016

Trapping Phenomenon Attenuates Tipping Points for Limit Cycles

Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the systems parameters abruptly shift the system to an alternative state with a contrasting dynamical behavior. While tipping in a fold bifurcation of an equilibrium is well understood, much less is known about tipping of oscillations (limit cycles) though this dynamics are the typical response of many natural systems to a periodic external forcing, like e.g. seasonal forcing in ecology and climate sciences. We provide a detailed analysis of tipping phenomena in periodically forced systems and show that, when limit cycles are considered, a transient structure, so-called channel, plays a fundamental role in the transition. Specifically, we demonstrate that trajectories crossing such channel conserve, for a characteristic time, the twisting behavior of the stable limit cycle destroyed in the fold bifurcation of cycles. As a consequence, this channel acts like a ghost of the limit cycle destroyed in the critical transition and instead of the expected abrupt transition we find a smooth one. This smoothness is also the reason that it is difficult to precisely determine the transition point employing the usual indicators of tipping points, like critical slowing down and flickering.

nlin.CD↗