Karin Alfaro

Pontifical Catholic University of Valparaíso | PUCV · Institute of Physics

Nonreciprocal coupling can alter the transport properties of material media, producing striking phenomena such as unidirectional amplification of waves, boundary modes, or self-assembled pattern formation. It is responsible for nonlinear convective instabilities in nonlinear systems that drive topological dissipative solitons in a single direction,...

The propagation of nonlinear waves, such as fires, weather fronts, and disease spread, has drawn attention since the dawn of time. A well-known example of nonlinear wave–fronts–in our daily lives is the domino waves, which propagate equally toward the left or right flank due to their reciprocal coupling. However, there are other situations where fr...

Symmetries in a network regulate its organization into functional clustered states. Given a generic ensemble of nodes and a desirable cluster (or group of clusters), we exploit the direct connection between the elements of the eigenvector centrality and the graph symmetries to generate a network equipped with the desired cluster(s), with such a syn...

Nonreciprocally coupled systems present rich dynamical behavior such as unidirectional amplification, fronts, localized states, pattern formation, and chaotic dynamics. Fronts are nonlinear waves that may connect an unstable equilibrium with a stable one and can suffer a convective instability when the coupling is nonreciprocal. Namely, a state inv...

A wealth of evidence shows that real-world networks are endowed with the small-world property, i.e., that the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. In addition, most social networks are organized so that no individual is more than six connections apart from any other, an empiric...

We study the synchronization properties of a generic networked dynamical system, and show that, under a suitable approximation, the transition to synchronization can be predicted with the only help of eigenvalues and eigenvectors of the graph Laplacian matrix. The transition comes out to be made of a well defined sequence of events, each of which c...

Symmetries in a network regulate its organization into functional clustered states. Given a generic ensemble of nodes and a desirable cluster (or group of clusters), we exploit the direct connection between the elements of the eigenvector centrality and the graph symmetries to generate a network equipped with the desired cluster(s), with such a syn...

Coupled excitable microlasers have been shown theoretically to sustain saltatory propagation of solitonic-like excitations and hold good promise for fabrication of advanced and integrated photonic processing circuits. By studying a model for evanescently coupled excitable microlaser lattices with integrated saturable absorber, we investigate how pu...

Boolean logic is the paradigm through which modern computation is performed in silica. When nonlinear dynamical systems are interacting in a directed graph, we show that computation abilities emerge spontaneously from adaptive synchronization, which actually can emulate Boolean logic. Precisely, we demonstrate that a single dynamical unit, a spikin...

In our more and more interconnected world, a specific risk is that of a cyber-epidemic (or cyber-pandemic), produced either accidentally or intentionally, where a cyber virus propagates from device to device up to undermining the global Internet system with devastating consequences in terms of economic costs and societal harms related to the shutdo...

We give evidence that consecutive explosive transitions may occur in two-layered networks, when a dynamical layer made of an ensemble of networking phase oscillators interacts with an environmental layer of oscillators which are in a state of approximate synchronization. Under these conditions, the interlayer coupling induces two consecutive explos...

We give evidence that a population of pure contrarian globally coupled D-dimensional Kuramoto oscillators reaches a collective synchronous state when the interplay between the units goes beyond the limit of pairwise interactions. Namely, we will show that the presence of higher-order interactions may induce the appearance of a coherent state even w...

The propagation of information in social, biological and technological systems represents a crucial component in their dynamic behavior. When limited to pairwise interactions, a rather firm grip is available on the relevant parameters and critical transitions of these spreading processes, most notably the pandemic transition, which indicates the co...

Coupled oscillators have been used to study synchronization in a wide range of social, biological, and physical systems, including pedestrian-induced bridge resonances, coordinated lighting up of firefly swarms, and enhanced output peak intensity in synchronizing laser arrays. Here we advance this subject by studying a variant of the Kuramoto model...

Over the past two decades, complex network theory provided the ideal framework for investigating the intimate relationships between the topological properties characterizing the wiring of connections among a system's unitary components and its emergent synchronized functioning. An increased number of setups from the real world found therefore a rep...

In this letter, we report preliminary experimental evidence of the role of local and global information on networks of a repeated Prisoner’s dilemma game. Namely, we consider three groups of players. In groups one and two, the selection of the game strategies is made upon knowledge of local and global information, respectively. In group three, inst...

Elucidating the mechanisms that lead to the emergence, evolution, and survival of cooperation in natural systems is still one of the main scientific challenges of current times. During the last three decades, theoretical and computational models as well as experimental data have made it possible to unveil and explain, from an evolutionary perspecti...

Identifying the most influential nodes in networked systems is vital to optimize their function and control. Several scalar metrics have been proposed to that effect, but the recent shift in focus towards higher-order networks has rendered them void of performance guarantees. We propose a new measure of node's centrality, which is no longer a scala...

Symmetries in a network connectivity regulate how the graph’s functioning organizes into clustered states. Classical methods for tracing the symmetry group of a network require very high computational costs, and therefore they are of hard, or eve impossible, execution for large sized graphs. We here unveil that there is a direct connection between...

We give evidence that a population of pure contrarians globally coupled D-dimensional Kuramoto oscillators reaches a collective synchronous state when the interplay between the units goes beyond the limit of pairwise interactions. An exact solution for the description of the microscopic dynamics for forward and backward transitions is provided, whi...

The propagation of information in social, biological and technological systems represents a crucial component in their dynamic behavior. When limited to pairwise interactions, a rather firm grip is available on the relevant parameters and critical transitions of these spreading processes, most notably the pandemic transition, which indicates the co...

Chains of coupled oscillators exhibit energy propagation by means of waves, pulses, and fronts. Nonreciprocal coupling radically modifies the wave dynamics of chains. Based on a prototype model of nonlinear chains with nonreciprocal coupling to nearest neighbors, we study nonlinear wave dynamics. Nonreciprocal coupling induces a convective instabil...

Coupled oscillators have been used to study synchronization in a wide range of social, biological, and physical systems, including pedestrian-induced bridge resonances, coordinated lighting up of firefly swarms, and enhanced output peak intensity in synchronizing laser arrays. Here we advance this subject by studying a variant of the Kuramoto model...

From biology to social science, the functioning of a wide range of systems is the result of elementary interactions which involve more than two constituents, so that their description has unavoidably to go beyond simple pairwise-relationships. Simplicial complexes are therefore the mathematical objects providing a faithful representation of such sy...

Collaboration patterns offer important insights into how scientific breakthroughs and innovations emerge in small and large research groups. However, links in traditional networks account only for pairwise interactions, thus making the framework best suited for the description of two-person collaborations, but not for collaborations in larger group...

The past two decades have seen significant successes in our understanding of networked systems, from the mapping of real-world networks to the establishment of generative models recovering their observed macroscopic patterns. These advances, however, are restricted to pairwise interactions and provide limited insight into higher-order structures. S...

Elucidating the mechanisms that lead to cooperation is still one of the main scientific challenges of current times, as many common cooperative scenarios remain elusive and at odds with Darwin's natural selection theory. Here, we study evolutionary games on populations that are structured beyond pairwise interactions. Specifically, we introduce a g...

Collective behavior, from murmurations to synchronized beating of heart cells, governs some of the most beautiful and important aspects of nature. Likewise, cooperation - the act of sacrificing personal benefits for the common good - is one of the pillars of social evolution, and it is the basis for the emergence of collective organized actions fro...

From biology to social science, the functioning of a wide range of systems is the result of elementary interactions which involve more than two constituents, so that their description has unavoidably to go beyond simple pairwise-relationships. Simplicial complexes are therefore the mathematical objects providing a faithful representation of such sy...

Nonlinear pulse propagation is a major feature in continuously extended excitable systems. The persistence of this phenomenon in coupled excitable systems is expected. Here, we investigate theoretically the propagation of nonlinear pulses in a 1D array of evanescently coupled excitable semiconductor lasers. We show that the propagation of pulses is...

The past two decades have seen significant successes in our understanding of complex networked systems, from the mapping of real-world social, biological and technological networks to the establishment of generative models recovering their observed macroscopic patterns. These advances, however, are restricted to pairwise interactions, captured by d...

Homogeneously driven dynamical systems exhibit multistability. Depending on the initial conditions, fronts present a rich dynamical behavior between equilibria. Qualitatively, this phenomenology is persistent under spatially modulated forcing. However, the understanding of equilibria and front dynamics organization is not fully established. Here, w...

Coupled oscillators can exhibit complex spatiotemporal dynamics. Here, we study the propagation of nonlinear waves into an unstable state in dissipative coupled oscillators. To this, we consider the dissipative Frenkel–Kontorova model, which accounts for a chain of coupled pendulums or Josephson junctions and coupling superconducting quantum interf...

We review experimental and theoretical results on the computing properties of single spiking micropillar lasers and present numerical studies of propagation and computing in chains of evanescently coupled micropillar lasers. Single micropillar lasers are shown to behave as ultrafast optical neurons with sub-nanosecond spike times. They also possess...

We report experimental and theoretical results on the lateral wet oxidation of bidimensional thin aluminum-rich layers into AlOx. We introduce a reaction-diffusion model of oxidation front propagation that includes effects of anisotropies and compare it to experimental results. This model can be used with any starting geometry, possibly nonconvex,...

Spatially forced systems can exhibit coexistence and a rich interface dynamics between manipulable states. We show here how the propagation speed of a front into an unstable state can be modified through periodic space forcing. Based on optical feedback, we set up a quasi-one-dimensional forced experiment in a liquid-crystal cell. When changing the...

Coupled dissipative nonlinear oscillators exhibit complex spatiotemporal dynamics. Frenkel-Kontorova is a prototype model of coupled nonlinear oscillators, which exhibits coexistence between stable and unstable state. This model accounts for several physical systems such as the movement of atoms in condensed matter and magnetic chains, dynamics of...