Manuel A. Matías

Spectrum of genetic diversity and networks of clonal organisms

Clonal reproduction characterizes a wide range of species including clonal plants in terrestrial and aquatic ecosystems, and clonal microbes such as bacteria and parasitic protozoa, with a key role in human health and ecosystem processes. Clonal organisms present a particular challenge in population genetics because, in addition to the possible existence of replicates of the same genotype in a given sample, some of the hypotheses and concepts underlying classical population genetics models are irreconcilable with clonality. The genetic structure and diversity of clonal populations were examined using a combination of new tools to analyse microsatellite data in the marine angiosperm Posidonia oceanica. These tools were based on examination of the frequency distribution of the genetic distance among ramets, termed the spectrum of genetic diversity (GDS), and of networks built on the basis of pairwise genetic distances among genets. Clonal growth and outcrossing are apparently dominant processes, whereas selfing and somatic mutations appear to be marginal, and the contribution of immigration seems to play a small role in adding genetic diversity to populations. The properties and topology of networks based on genetic distances showed a ‘small-world’ topology, characterized by a high degree of connectivity among nodes, and a substantial amount of substructure, revealing organization in subfamilies of closely related individuals. The combination of GDS and network tools proposed here helped in dissecting the influence of various evolutionary processes in shaping the intra-population genetic structure of the clonal organism investigated; these therefore represent promising analytical tools in population genetics.

Excitability mediated by localized structures in a dissipative nonlinear optical cavity

This work reports on a new regime of excitability associated to the existence of localized structures in a nonlinear optical system. Findings emphasize that, in absence of spatial degreed of freedom, the system described by the partial differential equation is not an excitable system. The system exhibits excitability only after a localized structure has undergone a Hopf and a saddle-loop bifurcation. Finally, this study shows that all this scenario is organized by a co-dimension two Takens-Bogdanov bifurcation point.

Dynamical instabilities of dissipative solitons in nonlinear optical cavities with nonlocal materials

In this work we characterize the dynamical instabilities of localized structures exhibited by a recently introduced [Gelens et al., Phys. Rev. A 75, 063812 (2007)] generalization of the Lugiato-Lefever model that includes a weakly nonlocal response of an intracavity metamaterial. A rich scenario, in which the localized structures exhibit different types of oscillatory instabilities, tristability, and excitability, including a regime of conditional excitability in which the system is bistable, is presented and discussed. Finally, it is shown that the scenario is organized by a pair of Takens-Bogdanov codimension-2 points.

Phase-space structure of two-dimensional excitable localized structures

In this work we characterize in detail the bifurcation leading to an excitable regime mediated by localized structures in a dissipative nonlinear Kerr cavity with a homogeneous pump. Here we show how the route can be understood through a planar dynamical system in which a limit cycle becomes the homoclinic orbit of a saddle point (saddle-loop bifurcation). The whole picture is unveiled, and the mechanism by which this reduction occurs from the full infinite-dimensional dynamical system is studied. Finally, it is shown that the bifurcation leads to an excitability regime, under the application of suitable perturbations. Excitability is an emergent property for this system, as it emerges from the spatial dependence since the system does not exhibit any excitable behavior locally.

Experimental study of the transitions between synchronous chaos and a periodic rotating wave

In this work we characterize experimentally the transition between periodic rotating waves and synchronized chaos in a ring of unidirectionally coupled Lorenz oscillators by means of electronic circuits. The study is complemented by numerical and theoretical analysis, and the intermediate states and their transitions are identified. The route linking periodic behavior with synchronous chaos involves quasiperiodic behavior and a type of high-dimensional chaos known as chaotic rotating wave. The high-dimensional chaotic behavior is characterized, and is shown to be composed actually by three different behaviors. The experimental study confirms the robustness of this route.

Dissipative soliton excitability induced by spatial inhomogeneities and drift

Disipative solitons (DS) arise in a large variety of systems from a balance between nonlinearity and spatial coupling, and driving and dissipation. In this work [1] we present a mechanism that generically induces dynamical regimes, such as oscillations and excitable behavior, in which the structure of the DS is preserved. The mechanism relies on the interplay between spatial inhomogeneities and drift, and therefore can be implemented under very general conditions.

Drifting instabilities of cavity solitons in vertical-cavity surface-emitting lasers with frequency-selective feedback

In this paper we study the formation and dynamics of self-propelled cavity solitons (CSs) in a model for vertical-cavity surface-emitting lasers (VCSELs) subjected to external frequency-selective feedback and build their bifurcation diagram for the case where carrier dynamics is eliminated. For low pump currents, we find that they emerge from the modulational instability point of the trivial solution, where traveling waves with a critical wave number are formed. For large currents, the branch of self-propelled solitons merges with the branch of resting solitons via a pitchfork bifurcation. We also show that a feedback phase variation of (2) can transform a CS (whether resting or moving) into a different one associated to an adjacent longitudinal external cavity mode. Finally, we investigate the influence of the carrier dynamics, relevant for VCSELs. We find and analyze qualitative changes in the stability properties of resting CSs when increasing the carrier relaxation time. In addition to a drifting instability of resting CSs, a distinctive kind of instability appears for certain ranges of carrier lifetime, leading to a swinging motion of the CS center position. Furthermore, for carrier relaxation times typical of VCSELs the system can display multistability of CSs.

Global dynamics of oscillator populations under common noise

Common noise acting on a population of identical oscillators can synchronize them. We develop a description of this process which is not limited to the states close to synchrony, but provides a global picture of the evolution of the ensembles. The theory is based on the Watanabe-Strogatz transformation, allowing us to obtain closed stochastic equations for the global variables. We show that at the initial stage, the order parameter grows linearly in time, while at the later stages the convergence to synchrony is exponentially fast. Furthermore, we extend the theory to nonidentical ensembles with the Lorentzian distribution of natural frequencies and determine the stationary values of the order parameter in dependence on driving noise and mismatch.

All Optical Logical Operations Using Excitable Cavity Solitons

We show theoretically that dissipative solitons arising in the transverse plane of nonlinear optical cavities show oscillatory and excitable regimes that can be used to perform all-optical logical operations. This allows for the construction of reconfigurable optical gates that can operate in parallel.

Excitability Mediated by Dissipative Solitons in Nonlinear Optical Cavities

Cavity solitons, which are dissipative solitons with a finite extension that appear in the transverse plane of nonlinear optical cavities, have been advocated for use in fast and compact optical information storage. We discuss the instabilities that can affect cavity solitons appearing in Kerr cavities. In particular, cavity solitons may exhibit a Hopf bifurcation leading to self-pulsating behavior, which is then followed by the destruction of the oscillation in a saddle-loop bifurcation. Beyond this point, there is a regime of excitable cavity solitons which appear when suitable perturbations are applied. Excitability is characterized by the nonlinear response of the system upon the application of an external stimulus. Only stimuli exceeding a threshold value are able to elicit a full and well-defined response in the system. In the case of cavity solitons, excitability emerges from the spatial dependence, since the system does not exhibit any excitable behavior locally. We demonstrate the existence of two different mechanisms which lead to excitability, pending on the profile of the pump field.