arXiv subjects

Marcelo A. Pires

Publications and source records attributed to Marcelo A. Pires.

At least 19 recordsLinked to original sources

arXiv2026

Tricriticality and chaos in a generalized Allee-logistic map

We present a novel nonlinear dynamical model, the generalized Allee-logistic (GAL) map given by $x_{t+1} = r x_t (1 - x_t) G(x_t)$ where $G(x_t) = m (x_t - h) + 1 - m$ incorporates the Allee effect with magnitude $m$ and threshold $h$. The case $m = 0$ yields the logistic map with a continuous transition to extinction. Conversely, $m = 1$ recovers a previously studied model that undergoes only a discontinuous extinction-to-active transition. Between these extremes, the GAL map exhibits nontrivial phenomena, including tricriticality with a closed-form expression for the tricritical point and a universal crossover function. Under a small external input, we verify Widom-like relations. We also note that the Allee effect disfavors the onset of chaos. Our work establishes additional bridges between analytically tractable chaotic maps, nonequilibrium tricriticality, and Allee effects.

nlin.CD↗

arXiv2026

Directionality and quantum backfire in continuous-time quantum walks from delocalized states: Exact results

We derive analytical results for continuous-time quantum walks from a new class of initial states with tunable delocalization. The dynamics are governed by a Hamiltonian with complex hopping amplitudes. We provide closed-form equations for key observables, revealing three notable findings: (1) the emergence of directed quantum transport from completely unbiased initial conditions; (2) a quantum backfire effect, where greater initial delocalization enhances short-time spreading but counterintuitively induces a comparatively smaller long-time spreading after a crossing time $t_{\mathrm{cross}}$; and (3) an exact characterization of survival probability, showing that the transition to an enhanced $t^{-3}$ decay is a fine-tuned effect. Our work establishes a comprehensive framework for controlling quantum transport through the interplay between intermediate initial delocalization and Hamiltonian phase.

quant-ph↗

arXiv2026

Chaos and Parrondo's paradox: An overview

Parrondo's paradox (PP) is a fundamental principle in nonlinear science where the alternation of individually losing strategies leads to a winning outcome. In this topical review, we provide the first systematic panorama of the synergy between PP and chaos. We observe a bidirectional connection between the two areas. The first direction is the translation of PP into the interplay between Order and Chaos through either Chaos + Chaos $\to$ Order (CCO) or Order + Order $\to$ Chaos (OOC). In this vein, many quantifiers, such as Lyapunov Exponents, $λ$, and entropic measures, are used. Second, we note that chaos can be used to engineer switching protocols that can lead to nontrivial effects in diverse PP cases. Our review clarifies the universality of PP and highlights its robust theoretical and practical applications across several areas of science and technology. Finally, we delineate key open questions, emphasizing the unresolved theoretical limits, the role of high-dimensional maps and continuous flows, and the critical need for more experimental verification of the dynamic PP in chaotic systems. For completeness, we also provide a full Python code that allows the reader to observe the many facets of the PP.

nlin.CD↗

arXiv2025

Enhanced spreading in continuous-time quantum walks using aperiodic temporal modulation of defects

Parrondo's paradox, where the alternation of two losing strategies can produce a winning outcome, has recently been demonstrated in continuous-time quantum walks (CTQWs) through periodic defect modulation. We extend this phenomenon to aperiodic protocols. We show that deterministic, non-repetitive defect switching can enhance quantum spreading in CTQWs compared to the defect-free case. Furthermore, we establish that the degree of this enhancement is strongly influenced by the autocorrelation and persistence characteristics of the applied aperiodic sequence. Our findings indicate that aperiodic defect modulation reliably maintains Parrondo's effect and provides new ways to control wavepacket properties in CTQWs.

quant-ph↗

arXiv2025

Composing $α$-Gauss and logistic maps: Gradual and sudden transitions to chaos

We introduce the $α$-Gauss-Logistic map, a new nonlinear dynamics constructed by composing the logistic and $α$-Gauss maps. Explicitly, our model is given by $x_{t+1} = f_L(x_t)x_t^{-α} - \lfloor f_L(x_t)x_t^{-α} \rfloor $ where $f_L(x_t) = r x_t (1-x_t)$ is the logistic map and $ \lfloor \ldots \rfloor $ is the integer part function. Our investigation reveals a rich phenomenology depending solely on two parameters, $r$ and $α$. For $α< 1$, the system exhibits multiple period-doubling cascades to chaos as the parameter $r$ is increased, interspersed with stability windows within the chaotic attractor. In contrast, for $1 \leq α< 2$, the onset of chaos is abrupt, occurring without any prior bifurcations, and the resulting chaotic attractors emerge without stability windows. For $α\geq 2$, the regular behavior is absent. The special case of $α= 1$ allows an analytical treatment, yielding a closed-form formula for the Lyapunov exponent and conditions for an exact uniform invariant density, using the Perron-Frobenius equation. Chaotic regimes for $α= 1$ can exhibit gaps or be gapless. Surprisingly, the golden ratio $Φ$ marks the threshold for the disappearance of the largest gap in the regime diagram. Additionally, at the edge of chaos in the abrupt transition regime, the invariant density approaches a $q$-Gaussian with $q=2$, which corresponds to a Cauchy distribution.

nlin.CD↗

arXiv2025

Cryptocurrency Time Series on the Binary Complexity-Entropy Plane: Ranking Efficiency from the Perspective of Complex Systems

We report the first application of a tailored Complexity-Entropy Plane designed for binary sequences and structures. We do so by considering the daily up/down price fluctuations of the largest cryptocurrencies in terms of capitalization (stable-coins excluded) that are worth $circa \,\, 90 \%$ of the total crypto market capitalization. With that, we focus on the basic elements of price motion that compare with the random walk backbone features associated with mathematical properties of the Efficient Market Hypothesis. From the location of each crypto on the Binary Complexity-Plane (BiCEP) we define an inefficiency score, $\mathcal I$, and rank them accordingly. The results based on the BiCEP analysis, which we substantiate with statistical testing, indicate that only Shiba Inu (SHIB) is significantly inefficient, whereas the largest stake of crypto trading is reckoned to operate in close-to-efficient conditions. Generically, our $\mathcal I$-based ranking hints the design and consensus architecture of a crypto is at least as relevant to efficiency as the features that are usually taken into account in the appraisal of the efficiency of financial instruments, namely canonical fiat money. Lastly, this set of results supports the validity of the binary complexity analysis.

q-fin.ST↗

arXiv2025

Parrondo's effects with aperiodic protocols

In this work, we study the effectiveness of employing archetypal aperiodic sequencing -- namely Fibonacci, Thue-Morse, and Rudin-Shapiro -- on the Parrondian effect. From a capital gain perspective, our results show that these series do yield a Parrondo's Paradox with the Thue-Morse based strategy outperforming not only the other two aperiodic strategies but benchmark Parrondian games with random and periodical ($AABBAABB\ldots$) switching as well. The least performing of the three aperiodic strategies is the Rudin-Shapiro. To elucidate the underlying causes of these results, we analyze the cross-correlation between the capital generated by the switching protocols and that of the isolated losing games. This analysis reveals that a strong anticorrelation with both isolated games is typically required to achieve a robust manifestation of Parrondo's effect. We also study the influence of the sequencing on the capital using the lacunarity and persistence measures. In general, we observe that the switching protocols tend to become less performing in terms of the capital as one increases the persistence and thus approaches the features of an isolated losing game. For the (log-)lacunarity, a property related to heterogeneity, we notice that for small persistence (less than 0.5) the performance increases with the lacunarity with a maximum around 0.4. In respect of this, our work shows that the optimization of a switching protocol is strongly dependent on a fine-tuning between persistence and heterogeneity.

physics.soc-ph↗

arXiv2023

Tricritical behavior in epidemic dynamics with vaccination

We scrutinize the phenomenology arising from a minimal vaccination-epidemic (MVE) dynamics using three methods: mean-field approach, Monte Carlo simulations, and finite-size scaling analysis. The mean-field formulation reveals that the MVE model exhibits either a continuous or a discontinuous active-to-absorbing phase transition, accompanied by bistability and a tricritical point. However, on square lattices, we detect no signs of bistability, and we disclose that the active-to-absorbing state transition has a scaling invariance and critical exponents compatible with the continuous transition of the directed percolation universality class. Additionally, our findings indicate that the tricritical and crossover behaviors of the MVE dynamics belong to the universality class of mean-field tricritical directed percolation.

physics.soc-ph↗

arXiv2023

Phase transition in the Galam's majority-rule model with information-mediated independence

We study the Galam's majority-rule model in the presence of an independent behavior that can be driven intrinsically or can be mediated by information regarding the collective opinion of the whole population. We first apply the mean-field approach where we obtained an explicit time-dependent solution for the order parameter of the model. We complement our results with Monte Carlo simulations where our findings indicate that independent opinion leads to order-disorder continuous nonequilibrium phase transitions. Finite-size scaling analysis show that the model belongs to the mean-field Ising model universality class. Moreover, results from an approach with the Kramers-Moyal coefficients provide insights about the social volatility.

cond-mat.stat-mech↗

arXiv2023

Quantum walks with spatiotemporal fractal disorder

We investigate the transport and entanglement properties exhibited by quantum walks with coin operators concatenated in a space-time fractal structure. Inspired by recent developments in photonics, we choose the paradigmatic Sierpinski gasket. The 0-1 pattern of the fractal is mapped into an alternation of the generalized Hadamard-Fourier operators. In fulfilling the blank space on the analysis of the impact of disorder in quantum walk properties -- specifically, fractal deterministic disorder --, our results show a robust effect of entanglement enhancement as well as an interesting novel road to superdiffusive spreading with a tunable scaling exponent attaining effective ballistic diffusion. Namely, with this fractal approach it is possible to obtain an increase in quantum entanglement without jeopardizing spreading. Alongside those features, we analyze further properties such as the degree of interference and visibility. The present model corresponds to a new application of fractals in an experimentally feasible setting, namely the building block for the construction of photonic patterned structures.

quant-ph↗

arXiv2022

Quantum walks in two dimensions: controlling directional spreading with entangling coins and tunable disordered step operator

We study a 2-D disordered time-discrete quantum walk based on 1-D `generalized elephant quantum walk' where an entangling coin operator is assumed and which paves the way to a new set of properties. We show that considering a given disorder in one direction, it is possible to control the degree of spreading and entanglement in the other direction. This observation helps assert that the random quantum walks of this ilk serve as a controllable decoherence channel with the degree of randomness being the tunable parameter and highlight the role of dimensionality in quantum systems regarding information and transport.

quant-ph↗

arXiv2022

Enhancing entanglement with the generalized elephant quantum walk from localized and delocalized states

Recently, it was introduced a generalization of a nonstandard step operator named the elephant quantum walk (EQW). With proper statistical distribution for the steps, that generalized EQW (gEQW) can be tuned to exhibit a myriad of dynamical scaling behavior ranging from standard diffusion to %and superdiffusion to ballistic and hyperballistic spreading. In this work, we study the influence of the statistics of the step size and the delocalization of the initial states on the entanglement entropy of the coin. Our results show that the gEQW generates maximally entangled states for almost all initial coin states and coin operators considering initially localized walkers and for the delocalized ones, taking the proper limit, the same condition is guaranteed. Differently from all the previous protocols that produce highly entangled states via QWs, this model is not upper-bounded by ballistic spreading and hence opens novel prospects for applications of dynamically disordered QWs as a robust maximal entanglement generator in programmable setups that ranges from slower-than-ballistic to faster-than ballistic.

quant-ph↗

arXiv2021

Double transition in kinetic exchange opinion models with activation dynamics

In this work we study a model of opinion dynamics considering activation/deactivation of agents. In other words, individuals are not static and can become inactive and drop out from the discussion. A probability $w$ governs the deactivation dynamics, whereas social interactions are ruled by kinetic exchanges, considering competitive positive/negative interactions. Inactive agents can become active due to interactions with active agents. Our analytical and numerical results show the existence of two distinct nonequilibrium phase transitions, with the occurrence of three phases, namely ordered (ferromagnetic-like), disordered (paramagnetic-like) and absorbing phases. The absorbing phase represents a collective state where all agents are inactive, i.e., they do not participate on the dynamics, inducing a frozen state. We determine the critical value $w_c$ above which the system is in the absorbing phase independently of the other parameters. We also verify a distinct critical behavior for the transitions among different phases.

physics.soc-ph↗

arXiv2021

Antivax movement and epidemic spreading in the era of social networks: Nonmonotonic effects, bistability and network segregation

In this work, we address a multicoupled dynamics on complex networks with tunable structural segregation. Specifically, we work on a networked epidemic spreading under a vaccination campaign with agents in favor and against the vaccine. Our results show that such coupled dynamics exhibits a myriad of phenomena such as nonequilibrium transitions accompanied by bistability. Besides we observe the emergence of an intermediate optimal segregation level where the community structure enhances negative opinions over vaccination but counterintuitively hinders - rather than favoring - the global disease spreading. Thus, our results hint vaccination campaigns should avoid policies that end up segregating excessively anti-vaccine groups so that they effectively work as echo chambers in which individuals look to confirmation without jeopardising the safety of the whole population.

physics.soc-ph↗

arXiv2021

What is the potential for a second peak in the evolution of SARS-CoV-2 in emerging and developing economies? Insights from a SIRASD model considering the informal economy

We study the potential scenarios from a Susceptible-Infected-Recovered-Asymptomatic-Symptomatic-Dead (SIRASD) model. As a novelty, we consider populations that differ in their degree of compliance with social distancing policies following socioeconomic attributes that are observed in emerging and developing countries. Considering epidemiological parameters estimated from data of the propagation of SARS-CoV-2 in Brazil -- where there is a significant stake of the population making their living in the informal economy and thus prone to not follow self-isolation -- we assert that if the confinement measures are lifted too soon, namely as much as one week of consecutive declining numbers of new cases, it is very likely the appearance of a second peak. Our approach should be valid for any country where the number of people involved in the informal economy is a large proportion of the total labor force. In summary, our results point out the crucial relevance of target policies for supporting people in the informal economy to properly comply with preventive measures during the pandemic.

q-bio.PE↗

arXiv2020

Diffusion plays an unusual role in ecological quasi-neutral competition in metapopulations

We investigate the phenomenology emerging from a 2-species dynamics under the scenario of a quasi-neutral competition within a metapopulation framework. We employ stochastic and deterministic approaches, namely spatially-constrained individual-based Monte Carlo simulations and coupled mean-field ODEs. Our results show the multifold interplay between competition, birth-death dynamics and spatial constraints induces a nonmonotonic relation between the ecological majority-minority switching and the diffusion between patches. This means that diffusion can set off birth-death ratios and enhance the preservation of a species.

q-bio.PE↗

arXiv2020

Negative correlations can play a positive role in disordered quantum walks

We investigate the emerging properties of quantum walks with temporal disorder engineered from a binary Markov chain with tailored correlation, $C$, and disorder strength, $r$. We show that when the disorder is weak -- $r \ll 1$ -- the introduction of negative correlation leads to a counter-intuitive higher production of spin-lattice entanglement entropy, $S_e$, than the setting with positive correlation, that is $S_e(-|C|)>S_e(|C|)$. These results show that negatively correlated disorder plays a more important role in quantum entanglement than it has been assumed in the literature.

quant-ph↗

arXiv2020

Quantum walks with sequential aperiodic jumps

We analyze a set of discrete-time quantum walks for which the displacements on a chain follow binary aperiodic jumps according to three paradigmatic sequences: Fibonacci, Thue-Morse and Rudin-Shapiro. We use a generalized Hadamard coin $\widehat C_{H}$ as well as a generalized Fourier coin $\widehat C_{K}$. We verify the QW experiences a slowdown of the wavepacket spreading --- $σ^2 (t) \sim t^α$ --- by the aperiodic jumps whose exponent, $α$, depends on the type of aperiodicity. Additional aperiodicity-induced effects also emerge, namely: (i) while the superdiffusive regime ($1<α<2$) is predominant, $α$ displays an unusual sensibility with the type of coin operator where the more pronounced differences emerge for the Rudin-Shapiro and random protocol; (ii) even though the angle $θ$ of the coin operator is homogeneous in space and time, there is a nonmonotonic dependence of $α$ with $θ$. Fingerprints of the aperiodicity in the hoppings are also found when additional distributional measures such as Shannon entropy, IPR, Jensen-Shannon dissimilarity, and kurtosis are computed. Finally, we argue the spin-lattice entanglement is enhanced by aperiodic jumps.

quant-ph↗