Discontinuity induced bifurcations of non-hyperbolic cycles in nonsmooth systems

We analyse three codimension-two bifurcations occurring in nonsmooth systems, when a non-hyperbolic cycle (fold, flip, and Neimark-Sacker cases, both in continuous- and discrete-time) interacts with one of the discontinuity boundaries characterising the system's dynamics. Rather than aiming at a complete unfolding of the three cases, which would require specific assumptions on both the class of nonsmooth system and the geometry of the involved boundary, we concentrate on the geometric features that are common to all scenarios. We show that, at a generic intersection between the smooth and discontinuity induced bifurcation curves, a third curve generically emanates tangentially to the former. This is the discontinuity induced bifurcation curve of the secondary invariant set (the other cycle, the double-period cycle, or the torus, respectively) involved in the smooth bifurcation. The result can be explained intuitively, but its validity is proven here rigorously under very general conditions. Three examples from different fields of science and engineering are also reported

Love stories can be unpredictable: Jules et Jim in the vortex of life

Love stories are dynamic processes that begin, develop, and often stay for a relatively long time in stationary or fluctuating regime, before possibly fading. Although they are, undoubtedly, the most important dynamic process in our life, they have only recently been cast in the formal frame of dynamical systems theory. In particular, why it is so difficult to predict the evolution of sentimental relationships continues to be largely unexplained. A common reason for this is that love stories reflect the turbulence of the surrounding social environment. But we can also imagine that the interplay of the characters involved contributes to make the story unpredictable, that is, chaotic. In other words, we conjecture that sentimental chaos can have a relevant endogenous origin. To support this intriguing conjecture, we mimic a real and well-documented love story with a mathematical model in which the environment is kept constant, and show that the model is chaotic. The case we analyze is the triangle described in Jules et Jim, an autobiographic novel by Henri-Pierr Roche that became famous worldwide after the success of the homonymous film directed by Fran8cois Truffaut

Red Queen Coevolution on Fitness Landscapes

Species do not merely evolve, they also coevolve with other organisms. Coevolution is a major force driving interacting species to continuously evolve ex- ploring their fitness landscapes. Coevolution involves the coupling of species fit- ness landscapes, linking species genetic changes with their inter-specific ecological interactions. Here we first introduce the Red Queen hypothesis of evolution com- menting on some theoretical aspects and empirical evidences. As an introduction to the fitness landscape concept, we review key issues on evolution on simple and rugged fitness landscapes. Then we present key modeling examples of coevolution on different fitness landscapes at different scales, from RNA viruses to complex ecosystems and macroevolution.Comment: 40 pages, 12 figures. To appear in "Recent Advances in the Theory and Application of Fitness Landscapes" (H. Richter and A. Engelbrecht, eds.). Springer Series in Emergence, Complexity, and Computation, 201

Controlling multistability in a vibro-impact capsule system

This is the final version of the article. Available from Springer Verlag via the DOI in this record.This work concerns the control of multistability in a vibro-impact capsule system driven by a harmonic excitation. The capsule is able to move forward and backward in a rectilinear direction, and the main objective of this work is to control such motion in the presence of multiple coexisting periodic solutions. A position feedback controller is employed in this study, and our numerical investigation demonstrates that the proposed control method gives rise to a dynamical scenario with two coexisting solutions, corresponding to forward and backward progression. Therefore, the motion direction of the system can be controlled by suitably perturbing its initial conditions, without altering the system parameters. To study the robustness of this control method, we apply numerical continuation methods in order to identify a region in the parameter space in which the proposed controller can be applied. For this purpose, we employ the MATLAB-based numerical platform COCO, which supports the continuation and bifurcation detection of periodic orbits of non-smooth dynamical systems.The second author has been supported by a Georg Forster Research Fellowship granted by the Alexander von Humboldt Foundation, Germany. The authors would like to thank Dr. Haibo Jiang for stimulating discussions and comments on this work

Species Invasion History Influences Community Evolution in a Tri-Trophic Food Web Model

Background: Recent experimental studies have demonstrated the importance of invasion history for evolutionary formation of community. However, only few theoretical studies on community evolution have focused on such views. Methodology and Principal Findings: We used a tri-trophic food web model to analyze the coevolutionary effects of ecological invasions by a mutant and by a predator and/or resource species of a native consumer species community and found that ecological invasions can lead to various evolutionary histories. The invasion of a predator makes multiple evolutionary community histories possible, and the evolutionary history followed can determine both the invasion success of the predator into the native community and the fate of the community. A slight difference in the timing of an ecological invasion can lead to a greatly different fate. In addition, even greatly different community histories can converge as a result of environmental changes such as a predator trait shift or a productivity change. Furthermore, the changes to the evolutionary history may be irreversible. Conclusions and Significance: Our modeling results suggest that the timing of ecological invasion of a species into a focal community can largely change the evolutionary consequences of the community. Our approach based on adaptive dynamics will be a useful tool to understand the effect of invasion history on evolutionary formation of community

Bacteriophage-mediated transfer of erythromycin and tetracycline resistance genes among group A streptococci

Objectives: In Streptococcus pyogenes (Group A Streptococcus, GAS), genes conferring efflux-mediated erythromycin (ERY) resistance (mefA/msr) are carried by functional prophages and may be associated with the tetracycline (TET) resistance determinant tetO. We sought to demonstrate the “ex vivo” lysogenic transfer of ERY and TET resistance genes among GAS. Methods: Forty-one ERY-susceptible GAS clinical isolates belonging to 12 different M-serotypes were used as recipients. The strain K56 (Mserotype 12) was used as a standard indicator to prepare lawns and as a model recipient, while the ERY- and TET-resistant strain m46 (Mserotype 4) was used as the donor of the tetO-mefA phage (phi-m46). The donor was induced with 0.2 mg/L mitomycin C. The culture supernatant was filtered, treated with DNAse/RNAse, concentrated by PEG/NaCl precipitation, and then added to cultures of the recipient strains. After incubation, these mixtures were either added to supplemented molten top agar and poured over BHI agar plates for the visualisation and counting of plaques or plated on BHI agar plus erythromycin for the selection of ERY-resistant lysogenic clones. PCR was used to check for the emm-type, mefA, and tetO genes before and after lysogenic transfer experiments, and to detect phi-m46 DNA in the supernatant of induced donor cultures. Results: The reference strain K56 and 85.4% (n = 35) of the clinical isolates acquired ERY/TET resistance when infected with purified phim46. All the M1 (n = 7), M12 (n = 6), M75 (n = 2), M18 (n = 1), M94 (n = 1) and a fraction of the M3 (5/7), M4 (1/3), M5 (1/2), M6 (4/7) strains were lysogenised and converted to the ERY/TET resistant phenotype. No lysogenic clones were isolated in the case of the M77, M78 and M89 recipients. Only M12 strains and the totality of them were phi-m46-sensitive. Conclusions: The erythromycin and tetracycline resistance determinants carried by phage-m46 can be efficiently transferred from a GAS strain to another by transduction. This is the first direct demonstration of phagemediated horizontal resistance gene transfer in S. pyogenes. In the set of strains analyzed, an M-serotype dependent barrier to lysogenic transfer was not observed. The exclusive lysis susceptibility of the M12 strains indicates that GAS with this serotype may represent the main responsible for the spread of this phage and the associated antibiotic resistance genes in S. pyogenes global population