arXiv subjects

Marcus A. M. de Aguiar

Publications and source records attributed to Marcus A. M. de Aguiar.

At least 19 recordsLinked to original sources

arXiv2026

Multistability and Juggling States in Frustrated Kuramoto Oscillators on Ring Networks

We study the properties of matrix coupled oscillators in ring networks and show that the system supports several families of synchronized clustered solutions. One of these families is characterized by consecutive oscillators belonging to distinct clusters, called alternate ordering, with two classes of solutions. The first consists of one or two static clusters, that lock on phases that depend on the coupling parameters, despite the non-zero natural oscillation frequency. The second one is comprised of clusters that rotate rigidly. The number of clusters depends on the neighbor connectivity. We also investigated sequential ordered clusters and showed that the constraints imposed by the interface oscillators imposes additional restrictions to equilibrium configurations. Although some of these solutions are stable, their basins of attraction depend on model parameters: when the system is initialized with random phases, the oscillators tend to organize themselves into dynamical clusters whose interfaces move along the ring. The oscillators within each cluster remain close to one of the stable phase configurations, while particles are exchanged at the interfaces. When interfaces moving in opposite directions collide, the corresponding clusters annihilate, until a state with interfaces moving in a common direction is reached.

nlin.PS↗

arXiv2026

Speciation by local adaptation and isolation by distance in extended environments

Speciation is often associated with geographical barriers that limit gene flow. However, species can also emerge in parapatry, even in homogeneous environments, through spatially restricted mating and limited dispersal. When the environment is not homogeneous, natural selection contributes to differentiation by local adaptation and tends to facilitate speciation. To explore how isolation by distance and adaptation combine to determine species diversity, we propose a model regulated by these two components. The former is implemented via mating restrictions on spatial proximity and genetic similarity, whereas the latter is realized by an ecological phenotype subjected to adaptation by natural selection. We consider a scenario where the environment has two distinct optima, and compare the resulting diversity patterns and phenotypic distributions with those of a homogeneous environment, with a single ecological optimum. We show that the interplay between selection and isolation by distance affects not only species formation but also phenotypic distributions and the timing of diversification. Simulating individuals with either restrictive or permissive mating regimes, combined with strong or weak selection, we show that: (i) environmental selection can accelerate diversification but is not always necessary for reproductive isolation; (ii) bimodal phenotypic patterns can arise through different evolutionary pathways and are therefore not necessarily signatures of ecological speciation; and (iii) when selection is weak and mating is restrictive, parapatric speciation begins before pronounced ecological differentiation, while the phenotypic peaks can oscillate and fail to reach a stationary state.

q-bio.PE↗

arXiv2026

Optimum foraging area in a three-trophic food chain

Organisms' foraging strategies are shaped by a trade-off between search area and local capture efficiency. This trade-off leads individuals to adapt their foraging area to an optimal value, impacting population dynamics. Here we study the effect of multiple foraging areas in a predator-prey model composed of three trophic levels. The interactions between predators and prey occur only within a limited neighborhood of the predators, where adaptation can occur over generations. We assume a trade-off where local predation efficiency is inversely proportional to the foraging area. These dynamics were implemented computationally via cellular automata and analytically via Master Equations with mean-field and pair approximations. Unlike the mean-field approximation, the pair approximation reproduced the dependence of population density on foraging area observed in the simulations. However, the simulations showed that the optimal foraging area does not maximize population density. Moreover, we found that a polymorphic population emerged, where not a single optimal strategy but a range of optimal strategies can coexist. Using the framework of Adaptive Dynamics, we confirm that the range of optimal areas is not the one that maximizes population size, but the Evolutionary Stable Strategy that can invade a population and not be invaded.

q-bio.PE↗

arXiv2026

Speciation, extinction and explosions induced by sudden environmental changes

We study the evolution of sexually reproducing populations subjected to sudden environmental changes. Using an individual based model we consider scenarios where abrupt changes can affect the carrying capacity, the mating range or the strength of assortativity, that controls the minimum similarity between individuals that allows mating to occur. We show that a boost in carrying capacity can either lead to new speciation events, thereby increasing biodiversity, or to widespread extinctions, causing the system to become dominated by a single species. A similar effect is observed with respect to the mating range. We show that the key factor determining the outcome of the process is genome length, i.e., the number of genes controlling reproduction and assortativity. We also show that when mating becomes more restrictive, increasing the degree of assortativity, a burst of speciation occurs. The explosion lasts only for a few generations, converging to values larger than before the change, but not as high as at the peak.

q-bio.PE↗

arXiv2026

What sets the critical genome length for sympatric speciation? A closed form and asymptotic theory

In the Derrida--Higgs model of sympatric speciation, a sexually reproducing population with finite binary genomes can mate only when the genetic overlap between two individuals exceeds a threshold $q_{\min}$. Depending on the genome length $L$, the population either remains genetically connected or fragments into reproductively isolated species. A central problem is therefore to predict the critical genome length $L_c$ at which fragmentation begins. At finite $L$, fluctuations broaden the overlap distribution and allow genetically distant regions of the population to remain connected. A previously proposed transient variance criterion captures this effect, but its evaluation requires numerical iteration of coupled moment equations. Here we first correct the unrestricted moment equations by removing a previously implicit assumption and then derive an explicit closed form expression for $L_c$. The resulting formula shows that the critical genome length is determined, at the time the mean overlap reaches $q_{\min}$, by the competition between deterministic separation from the unrestricted equilibrium and the transient genealogical variance of the overlap distribution. This expression permits a systematic asymptotic analysis. When the deterministic contribution dominates, $L_c$ becomes essentially independent of the population size $M$ and scales as $μ^{-2}$. When the transient genealogical variance dominates, $L_c$ grows as $M^{3/2}$ or as $\sqrt{M}/μ$, depending on how $M$ and the mutation rate $μ$ jointly vary. Simulations support all predicted behaviors. Our results identify transient genealogical variance as the principal mechanism linking finite genome fluctuations to the onset of reproductive fragmentation and provide a practical analytical prediction for the critical genome length.

q-bio.PE↗

arXiv2026

Collective Turns in Spinless Flocks

Using a minimal aggregation-based model, we address the efficient information transfer observed in natural flocks during collective turns. In our system, the turning signal emitted by a single individual propagates throughout the collective primarily at a constant speed. To characterize the source of this capability, we analyze the system in the continuum limit. Thus, we demonstrate that wave-propagating features arise solely from the non-reciprocal nature of interactions. We explore spectral anomalies that emerge due to this mechanism and provide an explanation through a perturbative analysis. Remarkably, within this scenario, the description of velocity fluctuations is found to follow a structure analogous to a Born approximation. Our model can be extended to study other physical contexts exhibiting polar order, and our arguments can be tested in natural systems.

nlin.AO↗

arXiv2026

Majority Correctness in Social Networks: From Well-Mixed Electorates to Complex Networks

We study majority correctness when voting is preceded by sustained social interaction on a social network. Motivated by the Condorcet Jury Theorem, we consider a binary choice with an objectively correct alternative, where uninformed voters revise their vote intentions through repeated interaction in the presence of competing committed leaders (zealots). In this zealot--contrarian voter model, voters may either imitate or oppose the views they encounter. For fully mixed electorates, we characterize the long-run distribution of votes and the correlation structure induced among voters, and we show that Erdős--Rényi networks exhibit the same majority-correctness behavior after an appropriate rescaling of leader influence. Building on these results, we establish a finite-electorate Condorcet-type guarantee: when post-deliberation individual correctness exceeds random choice, a strict majority is more likely to select the correct alternative than a randomly chosen voter. At the same time, we identify an aggregation failure: social interaction can reduce majority accuracy relative to a no-deliberation benchmark in which voters respond only to zealots. As the electorate size tends to infinity, this finite-electorate advantage disappears unless social updating is purely conformist, revealing a tipping point at full conformity: any persistent contrarian updating drives both individual and majority correctness to the random choice level of one half. Simulations on scale-free, ring, and small-world networks further show that topology matters because it shapes the vote correlations generated by social influence: hub-dominated structures generate stronger positive correlations and lower majority accuracy, whereas spatially structured networks generate weaker correlations, preserve a larger effective number of independent judgments, and improve majority accuracy.

cs.SI↗

arXiv2026

Modules as effective nodes in coarse-grained networks of Kuramoto oscillators

Most real-world networks exhibit a significant degree of modularity. Understanding the effects of such topology on dynamical processes is pivotal for advances in social and natural sciences. In this work we consider the dynamics of Kuramoto oscillators on modular networks and propose a simple coarse-graining procedure where modules are replaced by effective single oscillators. The method is inspired by EEG measurements, where very large groups of neurons under each electrode are interpreted as single nodes in a correlation network. We expose the interplay between intra-module and inter-module coupling strengths in keeping the coarse-graining process meaningful. We show that, when modules are well synchronized, the phase transition from asynchronous to synchronous motion in networks with 2 and 3 modules is very well described by their respective reduced systems, regardless of the network structure connecting the modules. Applications of the method to real networks with small modularity coefficients reveals that the approximation is also very accurate if oscillators in each module are identical. The method reproduces global synchronization patterns despite the low synchronizability of some modules, possibly allowing for the inference of the mean synchrony of each module when individual dynamics are not known.

nlin.AO↗

arXiv2026

Arnold tongues in the forced Kuramoto model with matrix coupling

We consider a generalization of the Kuramoto model in which phase oscillators are represented by unit vectors coupled by a matrix of constant coefficients. We show that, when the oscillators are driven by an external periodic force, several resonances appear, giving rise to Arnold tongues that can be observed as the intensity and frequency of the external force are varied. Applying the Ott-Antonsen ansatz we obtain equations for the module and phase of order parameter. As these equations are explicitly time-dependent, we resort to extensive numerical simulations to uncover the resonant modes and their associated Arnold tongues and devil's staircases. These results contrast with the original forced Kuramoto model, where only $1:1$ resonance is possible.

nlin.AO↗

arXiv2026

Interplay of sync and swarm: Theory and application of swarmalators

Swarmalators, entities that combine the properties of swarming particles with synchronized oscillations, represent a novel and growing area of research in the study of collective behavior. This review provides a comprehensive overview of the current state of swarmalator research, focusing on the interplay between spatial organization and temporal synchronization. After a brief introduction to synchronization and swarming as separate phenomena, we discuss the various mathematical models that have been developed to describe swarmalator systems, highlighting the key parameters that govern their dynamics. The review also discusses the emergence of complex patterns, such as clustering, phase waves, and synchronized states, and how these patterns are influenced by factors such as interaction range, coupling strength, and frequency distribution. Recently, some minimal models were proposed that are solvable and mimic real-world phenomena. The effect of predators in the swarmalator dynamics is also discussed. Finally, we explore potential applications in fields ranging from robotics to biological systems, where understanding the dual nature of swarming and synchronization could lead to innovative solutions. By synthesizing recent advances and identifying open challenges, this review aims to provide a foundation for future research in this interdisciplinary field.

nlin.AO↗

arXiv2026

The multi-allelic Moran process as a multi-zealot voter model: exact results and consequences for diversity thresholds

The Moran process is a foundational model of genetic drift and mutation in finite populations. In its standard two-allele form with population size $n$, allele counts, and hence allele frequencies, change through stochastic replacement and mutation, yet converge to a stationary distribution. This distribution undergoes a qualitative transition at the \emph{critical mutation rate} $μ_c=1/(2n)$: at $μ=μ_c$ it is exactly uniform, so that the probability of observing $k$ copies of allele~1 (and $n-k$ of allele~2) is $π(k)=1/(n+1)$ for $k=0,\dots,n$. For $μ<μ_c$ diversity is low: the stationary distribution places most of its mass near $k=0$ and $k=n$, and the population is therefore typically dominated by one allele. For $μ>μ_c$, on the other hand, diversity is high: the distribution concentrates around intermediate values, so that both alleles are commonly present at comparable frequencies. Recently, the two-allele Moran process was shown to be exactly equivalent to the voter model with two candidates and $α_1$ and $α_2$ committed voters (\emph{zealots}) in a population of $n+α_1+α_2$, where mutation is played by zealot influence. Here we extend this equivalence to multiple alleles and multiple candidates. Using the mapping, we derive the exact stationary distribution of allele counts for well-mixed populations with an arbitrary number $m$ of alleles, and obtain the critical mutation rate $μ_c = 1/(m+2n-2)$, which depends explicitly on $m$. We then analyze the Moran process on randomly connected populations and show that both the stationary distribution and $μ_c$ are invariant to network structure and coincide with the well-mixed results. Finally, simulations on general network topologies show that structural heterogeneity can substantially reshape the stationary allele distribution and, consequently, the level of genetic diversity.

q-bio.PE↗

arXiv2025

Generalizing Condorcet's Jury Theorem to Social Networks

We generalize Condorcet's jury theorem (CJT) to socially connected populations in which agents revise discrete choices on a network in the presence of zealots. Free agents receive privately informative signals about the correct alternative and, at each update, either retain their state or imitate a uniformly chosen neighbor (free or zealot). For finite networks, we derive closed-form stationary laws for vote counts, and we characterize the corresponding vote-share limits as the number of free voters tends to infinity. For majority rule -- both in binary and multi-alternative settings -- we obtain an exact accuracy limit in closed form via the regularized incomplete beta function. For plurality rule, we establish sharp closed-form lower bounds on accuracy, expressed in terms of regularized incomplete beta functions. Under an absolute-majority condition for the correct alternative, both majority and plurality accuracies strictly exceed the accuracy of any single voter, showing that informative signals, coupled through social interaction, are amplified at the group level. These results extend CJT beyond independence and provide closed-form accuracy benchmarks for networked decision systems in social, biological, and engineered settings.

physics.soc-ph↗

arXiv2025

Synchronization of identical oscillators on a sphere: exact results with external forces and higher-order interactions

We study the dynamics of the Kuramoto model on the sphere under higher-order interactions and an external periodic force. For identical oscillators, we introduce a novel way to incorporate three- and four-body interactions into the dynamics of the order parameter, allowing for a full dimensional reduction of this system. We discuss how such reduction can be implemented in two different ways and how they are related. When restricted to the equator, the dynamics is similar to that of the usual Kuramoto model, up to an interesting renormalization of the coupling constants. Outside this plane, the motion reduces to a two-parameter set of periodic orbits. We also locate the bifurcation curves of the system as functions of different parameters.

nlin.AO↗

arXiv2025

Emergence of Collective Accuracy in Socially Connected Networks

We analyze the accuracy of collective decision-making in socially connected populations, where agents update binary choices through local interactions on a network. Each agent receives a private signal that is biased -- even marginally -- toward the correct alternative, and social influence mediates the aggregation of these signals. We show analytically that, in the large-population limit, the probability of a correct majority converges to a nontrivial expression involving the regularized incomplete beta function. Remarkably, this collective accuracy surpasses that of any individual agent whenever private signals are better than random, revealing that network-mediated influence can enhance, rather than impair, group performance. Our findings may inform the design of resilient decision-making systems in social, biological, and engineered networks, where accuracy must emerge from interdependent and noisy agents.

stat.ME↗

arXiv2025

Exact solutions of the Kuramoto model with asymmetric higher order interactions of arbitrary order

Higher order interactions can lead to new equilibrium states and bifurcations in systems of coupled oscillators described by the Kuramoto model. However, even in the simplest case of 3-body interactions there are more than one possible functional forms, depending on how exactly the bodies are coupled. Which of these forms is better suited to describe the dynamics of the oscillators depends on the specific system under consideration. Here we show that, for a particular class of interactions, reduced equations for the Kuramoto order parameter can be derived for arbitrarily many bodies. Moreover, the contribution of a given term to the reduced equation does not depend on its order, but on a certain effective order, that we define. We give explicit examples where bi and tri-stability is found and discuss a few exotic cases where synchronization happens via a third order phase transition.

physics.soc-ph↗

arXiv2024

The transition to speciation in the finite genome Derrida-Higgs model: a heuristic solution

The process of speciation, where an ancestral species divides in two or more new species, involves several geographic, environmental and genetic components that interact in a complex way. Understanding all these elements at once is challenging and simple models can help unveiling the role of each factor separately. The Derrida-Higgs model describes the evolution of a sexually reproducing population subjected to mutations in a well mixed population. Individuals are characterized by a string with entries $\pm1$ representing a haploid genome with biallelic genes. If mating is restricted by genetic similarity, so that only individuals that are sufficiently similar can mate, sympatric speciation, i.e. the emergence of species without geographic isolation, can occur. Only four parameters rule the dynamics: population size $N$, mutation rate $μ$, minimum similarity for mating $q_{min}$ and genome size $B$. In the limit $B\rightarrow\infty$, speciation occurs if the simple condition $q_{min}>(1+4μN)^{-1}$ is satisfied. However, this condition fails for finite genomes, and speciation does not occur if the genome size is too small. This indicates the existence of a critical genome size for speciation. In this work, we develop an analytical theory of the distribution of similarities between individuals, a quantity that defines how tight or spread out is the genetic content of the population. This theory is carried out in the absence of mating restrictions, where evolution equations for the mean and variance of the similarity distribution can be derived. We then propose a heuristic description of the speciation transition which allows us to numerically calculate the critical genome size for speciation as a function of the other model parameters. The result is in good agreement with the simulations of the model and may guide further investigations on theoretical conditions for species formation.

q-bio.PE↗

arXiv2024

Bifurcations in the Kuramoto model with external forcing and higher-order interactions

Synchronization is an important phenomenon in a wide variety of systems comprising interacting oscillatory units, whether natural (like neurons, biochemical reactions, cardiac cells) or artificial (like metronomes, power grids, Josephson junctions). The Kuramoto model provides a simple description of these systems and has been useful in their mathematical exploration. Here we investigate this model combining two common features that have been observed in many systems: external periodic forcing and higher-order interactions among the elements. We show that the combination of these ingredients leads to a very rich bifurcation scenario that produces 11 different asymptotic states of the system, with competition between forced and spontaneous synchronization. We found, in particular, that saddle-node, Hopf and homoclinic manifolds are duplicated in regions of parameter space where the unforced system displays bi-stability.

nlin.AO↗

arXiv2024

Assortativity in sympatric speciation and species classification

We investigate the role of assortative mating in speciation using the sympatric model of Derrida and Higgs. The model explores the idea that genetic differences create incompatibilities between individuals, preventing mating if the number of such differences is too large. Speciation, however, only happens in this mating system if the number of genes is large. Here we show that speciation with small genome sizes can occur if assortative mating is introduced. In our model individuals are represented by three chromosomes: one responsible for reproductive compatibility, one for coding the trait on which assortativity will operate, and a neutral chromosome. Reproduction is possible if individuals are genetically similar with respect to the first chromosome, but among these compatible mating partners, the one with the most similar trait coded by the second chromosome is selected. We show that this type of assortativity facilitates speciation, which can happen with a small number of genes in the first chromosome. Species, classified according to reproductive isolation, dictated by the first chromosome, can display different traits values, as measured by the second and the third chromosomes. Therefore, species can also be identified based on similarity of the neutral trait, which works as a proxy for reproductive isolation.

q-bio.PE↗