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This work concerns the long-term collective excitability properties and the statistical analysis of the critical events displayed by a recently introduced spatiotemporal many-body model, proposed as a new paradigm for Artificial Life. Numerical simulations show that excitable collective structures emerge in the form of dynamic networks, created by bursts of spatiotemporal activity (avalanches) at the edge of a synchronization phase transition. The spatiotemporal dynamics is portraited by a movie and quantified by time varying collective parameters, showing that the dynamic networks undergo a "life cycle," made of self-creation, homeostasis, and self-destruction. The power spectra of the collective parameters show 1/f power law tails. The statistical properties of the avalanches, evaluated in terms of size and duration, show power laws with characteristic exponents in agreement with those values experimentally found in the neural networks literature. The mechanism underlying avalanches is argued in terms of local-to-collective excitability. The connections that link the present work to self-organized criticality, neural networks, and Artificial Life are discussed.

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This work concerns a many-body deterministic model that displays life-like properties such as emergence, complexity, self-organization, self-regulation, excitability and spontaneous compartmentalization. The model portraits the dynamics of an ensemble of locally coupled polar phase oscillators, moving in a two-dimensional space, that under certain conditions exhibit emergent superstructures. Those superstructures are self-organized dynamic networks, resulting from a synchronization process of many units, over length scales much greater than the interaction range. Such networks compartmentalize the two-dimensional space with no a priori constraints, due to the formation of porous transport walls, and represent a highly complex and novel non-linear behavior. The analysis is numerically carried out as a function of a control parameter showing distinct regimes: static pattern formation, dynamic excitable networks formation, intermittency and chaos. A statistical analysis is drawn to determine the control parameter ranges for the various behaviors to appear. The model and the results shown in this work are expected to contribute to the field of artificial life.

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In this work we show how global self-organized patterns can come out of a disordered ensemble of point oscillators, as a result of a deterministic, and not of a random, cooperative process. The resulting system dynamics has many characteristics of classical thermodynamics. To this end, a modified Kuramoto model is introduced, by including Euclidean degrees of freedom and particle polarity. The standard deviation of the frequency distribution is the disorder parameter, diversity, acting as temperature, which is both a source of motion and of disorder. For zero and low diversity, robust static phase-synchronized patterns (crystals) appear, and the problem reverts to a generic dissipative many-body problem. From small to moderate diversity crystals display vibrations followed by structure disintegration in a competition of smaller dynamic patterns, internally synchronized, each of which is capable to manage its internal diversity. In this process a huge variety of self-organized dynamic shapes is formed. Such patterns can be seen again as (more complex) oscillators, where the same description can be applied in turn, renormalizing the problem to a bigger scale, opening the possibility of pattern evolution. The interaction functions are kept local because our idea is to build a system able to produce global patterns when its constituents only interact at the bond scale. By further increasing the oscillator diversity, the dynamics becomes erratic, dynamic patterns show short lifetime, and finally disappear for high diversity. Results are neither qualitatively dependent on the specific choice of the interaction functions nor on the shape of the probability function assumed for the frequencies. The system shows a phase transition and a critical behaviour for a specific value of diversity.

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Semiconductor ring lasers display a variety of dynamical regimes originating from the nonlinear competition between the clockwise and counter-clockwise propagating modes. In particular, for large pumping the system has a bistable regime in which two stationary quasi-unidirectional counter-propagating modes coexist. Bistability is induced by cross-gain saturation of the two counter-propagating modes being stronger than the self-saturation and can be used for data storage when the semiconductor ring laser is addressed with an optical pulse. In this work we study the response time when an optical pulse is injected in order to make the system switch from one mode to the counter-propagating one. We also determine the optimal pulse energy to induce switching.

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We introduce a prototype model for globally coupled oscillators in which each element is given an oscillation frequency and a preferential oscillation direction (polarization), both randomly distributed. We found two collective transitions: to phase synchronization and to polarization ordering. Introducing a global-phase and polarization order parameters, we show that the transition to global-phase synchrony is found when the coupling overcomes a critical value and that polarization order enhancement cannot take place before global-phase synchrony. We develop a self-consistent theory to determine both order parameters in good agreement with numerical results.

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We show that self-pulsating vertical-cavity surface-emitting lasers can exhibit vectorial chaos, i.e., chaos in both intensity and polarization. The achievable synchronization degree of two such lasers is high when using a continuous control scheme and unidirectional coupling. We propose a novel encryption scheme, where the phase of the vectorial field is modulated. Therefore, the total intensity of these lasers remains synchronized while the intensities in the polarization modes (de)synchronize following the phase modulation at a ps time scale. This technique allows for transmission of secure data at high bit rates that are not limited by the relaxation oscillation frequency.

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We implement a dynamic model that describes the polarization behavior in vertical-cavity surface-emitting lasers that contain an absorbing region surrounding the active zone. We find four regions of qualitatively different behavior: stable linearly polarized operation, intensity pulsations of a linearly polarized component, pulsations of both total-intensity and polarization components, and polarization self-pulsation with constant total intensity. We characterize the four regions by computing the polarization-resolved optical and power spectra. The predicted behavior agrees with recent experimental results.