A deterministic model for non-monotone relationship between translation of upstream and downstream open reading frames.

Totally asymmetric simple exclusion process (TASEP) modelling was shown to offer a parsimonious explanation for the experimentally confirmed ability of a single upstream open reading frames (uORFs) to upregulate downstream translation during the integrated stress response. As revealed by numerical simulations, the model predicts that reducing the density of scanning ribosomes upstream of certain uORFs increases the flow of ribosomes downstream. To gain a better insight into the mechanism which ensures the non-monotone relation between the upstream and downstream flows, in this work, we propose a phenomenological deterministic model approximating the TASEP model of the translation process. We establish the existence of a stationary solution featuring the decreasing density along the uORF for the deterministic model. Further, we find an explicit non-monotone relation between the upstream ribosome density and the downstream flow for the stationary solution in the limit of increasing uORF length and increasingly leaky initiation. The stationary distribution of the TASEP model, the stationary solution of the deterministic model and the explicit limit are compared numerically.

Competing barnacle species with a time dependent reproduction rate.

A simple competition model with time varying periodic coefficients, in which two species use different reproduction strategies, is explored in this paper. The two species considered comprise a native species which reproduces once a year over a short time period and an invasive species which is capable of reproducing throughout the entire year. A monotonicity property of the model is instrumental for its analysis. The model reveals that the time difference between the peak of reproduction for the two species is a critical factor in determining the outcome of competition between these species. The impact of climate change and an anthropogenic disturbance, comprising the creation of additional substrate, is also investigated using a modified model. The results of this paper describe how climate change will favour the invasive species by reducing the time period between the reproductive peaks of the two species and how the addition of new substrates is likely to endanger a small population of either of the two species, depending on the timing of the introduction of the substrates.

Effect of dynamical instability on timing jitter in passively mode-locked quantum-dot lasers.

We study the effect of noise on the dynamics of passively mode-locked semiconductor lasers both experimentally and theoretically. A method combining analytical and numerical approaches for estimation of pulse timing jitter is proposed. We investigate how the presence of dynamical features such as wavelength bistability in a quantum-dot laser affects timing jitter.

Bistability and hysteresis in an optically injected two-section semiconductor laser.

The effect of coherent single frequency injection on two-section semiconductor lasers is studied numerically using a model based on a set of delay differential equations. The existence of bistability between different continuous-wave and nonstationary regimes of operation is demonstrated in the case of sufficiently large linewidth enhancement factors.

Analytical solution for a class of network dynamics with mechanical and financial applications.

We show that for a certain class of dynamics at the nodes the response of a network of any topology to arbitrary inputs is defined in a simple way by its response to a monotone input. The nodes may have either a discrete or continuous set of states and there is no limit on the complexity of the network. The results provide both an efficient numerical method and the potential for accurate analytic approximation of the dynamics on such networks. As illustrative applications, we introduce a quasistatic mechanical model with objects interacting via frictional forces and a financial market model with avalanches and critical behavior that are generated by momentum trading strategies.

Optically injected mode-locked laser.

We study analytically and numerically a delay differential model of a passively mode-locked semiconductor laser subjected to a single-frequency coherent injection. The width of the locking cone is calculated asymptotically in the limit of small injection and zero line-width enhancement factors and compared to that obtained by direct numerical integration of the model equations. The dependence of the locking cone on the laser parameters is discussed.

Nonlocal branches of cycles, bistability, and topologically persistent mixed mode oscillations.

A possible mechanism for generating mixed mode oscillations is based on an appropriate S-shaped structure, which graphs the relation between the parameter and the collection of periodic oscillations existing for a particular parameter value in the product of parameter and phase spaces. This natural scenario should be supplemented by simple and constructive criteria of existence, and methods of localization, of such S-shaped structures. These criteria are the main focus of the paper.

Excitability in a quantum dot semiconductor laser with optical injection.

We experimentally analyze the dynamics of a quantum dot semiconductor laser operating under optical injection. We observe the appearance of single- and double-pulse excitability at one boundary of the locking region. Theoretical considerations show that these pulses are related to a saddle-node bifurcation on a limit cycle as in the Adler equation. The double pulses are related to a period-doubling bifurcation and occur on the same homoclinic curve as the single pulses.