Coupled environmental and demographic fluctuations shape the evolution of cooperative antimicrobial resistance.

There is a pressing need to better understand how microbial populations respond to antimicrobial drugs, and to find mechanisms to possibly eradicate antimicrobial-resistant cells. The inactivation of antimicrobials by resistant microbes can often be viewed as a cooperative behaviour leading to the coexistence of resistant and sensitive cells in large populations and static environments. This picture is, however, greatly altered by the fluctuations arising in volatile environments, in which microbial communities commonly evolve.

Design of Linear Block Copolymers and Star Terpolymers That Produce Two Length Scales at Phase Separation.

Quasicrystals (materials with long-range order but without the usual spatial periodicity of crystals) were discovered in several soft matter systems in the last 20 years. The stability of quasicrystals has been attributed to the presence of two prominent length scales in a specific ratio, which is 1.93 for the 12-fold quasicrystals most commonly found in soft matter.

Rectangle-triangle soft-matter quasicrystals with hexagonal symmetry.

Aperiodic (quasicrystalline) tilings, such as Penrose's tiling, can be built up from, e.g., kites and darts, squares and equilateral triangles, rhombi- or shield-shaped tiles, and can have a variety of different symmetries.

How does homophily shape the topology of a dynamic network?

We consider a dynamic network of individuals that may hold one of two different opinions in a two-party society. As a dynamical model, agents can endlessly create and delete links to satisfy a preferred degree, and the network is shaped by homophily, a form of social interaction. Characterized by the parameter J∈[-1,1], the latter plays a role similar to Ising spins: agents create links to others of the same opinion with probability (1+J)/2 and delete them with probability (1-J)/2.

Deriving phase field crystal theory from dynamical density functional theory: Consequences of the approximations.

Phase field crystal (PFC) theory is extensively used for modeling the phase behavior, structure, thermodynamics, and other related properties of solids. PFC theory can be derived from dynamical density functional theory (DDFT) via a sequence of approximations. Here, we carefully identify all of these approximations and explain the consequences of each.

Survival behavior in the cyclic Lotka-Volterra model with a randomly switching reaction rate.

We study the influence of a randomly switching reproduction-predation rate on the survival behavior of the nonspatial cyclic Lotka-Volterra model, also known as the zero-sum rock-paper-scissors game, used to metaphorically describe the cyclic competition between three species. In large and finite populations, demographic fluctuations (internal noise) drive two species to extinction in a finite time, while the species with the smallest reproduction-predation rate is the most likely to be the surviving one (law of the weakest). Here we model environmental (external) noise by assuming that the reproduction-predation rate of the strongest species (the fastest to reproduce and predate) in a given static environment randomly switches between two values corresponding to more and less favorable external conditions.

Influence of Luddism on innovation diffusion.

We generalize the classical Bass model of innovation diffusion to include a new class of agents-Luddites-that oppose the spread of innovation. Our model also incorporates ignorants, susceptibles, and adopters. When an ignorant and a susceptible meet, the former is converted to a susceptible at a given rate, while a susceptible spontaneously adopts the innovation at a constant rate.

Characterization of spiraling patterns in spatial rock-paper-scissors games.

The spatiotemporal arrangement of interacting populations often influences the maintenance of species diversity and is a subject of intense research. Here, we study the spatiotemporal patterns arising from the cyclic competition between three species in two dimensions. Inspired by recent experiments, we consider a generic metapopulation model comprising "rock-paper-scissors" interactions via dominance removal and replacement, reproduction, mutations, pair exchange, and hopping of individuals.

Cyclic dominance in evolutionary games: a review.

Rock is wrapped by paper, paper is cut by scissors and scissors are crushed by rock. This simple game is popular among children and adults to decide on trivial disputes that have no obvious winner, but cyclic dominance is also at the heart of predator-prey interactions, the mating strategy of side-blotched lizards, the overgrowth of marine sessile organisms and competition in microbial populations. Cyclical interactions also emerge spontaneously in evolutionary games entailing volunteering, reward, punishment, and in fact are common when the competing strategies are three or more, regardless of the particularities of the game.

Cycling chaotic attractors in two models for dynamics with invariant subspaces.

Nonergodic attractors can robustly appear in symmetric systems as structurally stable cycles between saddle-type invariant sets. These saddles may be chaotic giving rise to "cycling chaos." The robustness of such attractors appears by virtue of the fact that the connections are robust within some invariant subspace.

Phase resetting effects for robust cycles between chaotic sets.

In the presence of symmetries or invariant subspaces, attractors in dynamical systems can become very complicated, owing to the interaction with the invariant subspaces. This gives rise to a number of new phenomena, including that of robust attractors showing chaotic itinerancy. At the simplest level this is an attracting heteroclinic cycle between equilibria, but cycles between more general invariant sets are also possible.

Infinities of stable periodic orbits in systems of coupled oscillators.

We consider the dynamical behavior of coupled oscillators with robust heteroclinic cycles between saddles that may be periodic or chaotic. We differentiate attracting cycles into types that we call phase resetting and free running depending on whether the cycle approaches a given saddle along one or many trajectories. At loss of stability of attracting cycling, we show in a phase-resetting example the existence of an infinite family of stable periodic orbits that accumulate on the cycling, whereas for a free-running example loss of stability of the cycling gives rise to a single quasiperiodic or chaotic attractor.