Stable scalable control of soliton propagation in broadband nonlinear optical waveguides

We develop a method for achieving scalable transmission stabilization and switching of $N$ colliding soliton sequences in optical waveguides with broadband delayed Raman response and narrowband nonlinear gain-loss. We show that dynamics of soliton amplitudes in $N$-sequence transmission is described by a generalized $N$-dimensional predator-prey model. Stability and bifurcation analysis for the predator-prey model are used to obtain simple conditions on the physical parameters for robust transmission stabilization as well as on-off and off-on switching of $M$ out of $N$ soliton sequences. Numerical simulations for single-waveguide transmission with a system of $N$ coupled nonlinear Schr\"odinger equations with $2 \le N \le 4$ show excellent agreement with the predator-prey model's predictions and stable propagation over significantly larger distances compared with other broadband nonlinear single-waveguide systems. Moreover, stable on-off and off-on switching of multiple soliton sequences and stable multiple transmission switching events are demonstrated by the simulations. We discuss the reasons for the robustness and scalability of transmission stabilization and switching in waveguides with broadband delayed Raman response and narrowband nonlinear gain-loss, and explain their advantages compared with other broadband nonlinear waveguides.Comment: 37 pages, 7 figures, Eur. Phys. J. D (accepted

Soliton-like phenomena in one-dimensional cross-diffusion systems: a predator-prey pursuit and evasion example

We have studied properties of nonlinear waves in a mathematical model of a predator-prey system with pursuit and evasion. We demonstrate a new type of propagating wave in this system. The mechanism of propagation of these waves essentially depends on the ``taxis'', represented by nonlinear ``cross-diffusion'' terms in the mathematical formulation. We have shown that the dependence of the velocity of wave propagation on the taxis has two distinct forms, ``parabolic'' and ``linear''. Transition from one form to the other correlates with changes in the shape of the wave profile. Dependence of the propagation velocity on diffusion in this system differs from the square-root dependence typical of reaction-diffusion waves. We demonstrate also that, for systems with negative and positive taxis, for example, pursuit and evasion, there typically exists a large region in the parameter space, where the waves demonstrate quasisoliton interaction: colliding waves can penetrate through each other, and waves can also reflect from impermeable boundaries.Comment: 15 pages, 18 figures, submitted to Physica

Moving forward in circles: challenges and opportunities in modelling population cycles

Population cycling is a widespread phenomenon, observed across a multitude of taxa in both laboratory and natural conditions. Historically, the theory associated with population cycles was tightly linked to pairwise consumer–resource interactions and studied via deterministic models, but current empirical and theoretical research reveals a much richer basis for ecological cycles. Stochasticity and seasonality can modulate or create cyclic behaviour in non-intuitive ways, the high-dimensionality in ecological systems can profoundly influence cycling, and so can demographic structure and eco-evolutionary dynamics. An inclusive theory for population cycles, ranging from ecosystem-level to demographic modelling, grounded in observational or experimental data, is therefore necessary to better understand observed cyclical patterns. In turn, by gaining better insight into the drivers of population cycles, we can begin to understand the causes of cycle gain and loss, how biodiversity interacts with population cycling, and how to effectively manage wildly fluctuating populations, all of which are growing domains of ecological research

Long-term change in benthopelagic fish abundance in the abyssal northeast Pacific Ocean

Food web structure, particularly the relative importance of bottom-up and top-down control of animal abundances, is poorly known for the Earth's largest habitats: the abyssal plains. A unique 15-yr time series of climate, productivity, particulate flux, and abundance of primary consumers (primarily echinoderms) and secondary consumers (fish) was examined to elucidate the response of trophic levels to temporal variation in one another. Towed camera sled deployments in the abyssal northeast Pacific (4100 m water depth) showed that annual mean numbers of the dominant fish genus (Coryphaenoides spp.) more than doubled over the period 1989-2004. Coryphaenoides spp. abundance was significantly correlated with total abundance of mobile epibenthic megafauna (echinoderms), with changes in fish abundance lagging behind changes in the echinoderms. Direct correlations between surface climate and fish abundances, and particulate organic carbon (POC) flux and fish abundances, were insignificant, which may be related to the varied response of the potential prey taxa to climate and POC flux. This Study provides a fare opportunity to study the long-term dynamics of an unexploited marine fish population and Suggests a dominant role for bottom-up control in this system

Pursuit-evasion predator-prey waves in two spatial dimensions

We consider a spatially distributed population dynamics model with excitable predator-prey dynamics, where species propagate in space due to their taxis with respect to each other's gradient in addition to, or instead of, their diffusive spread. Earlier, we have described new phenomena in this model in one spatial dimension, not found in analogous systems without taxis: reflecting and self-splitting waves. Here we identify new phenomena in two spatial dimensions: unusual patterns of meander of spirals, partial reflection of waves, swelling wavetips, attachment of free wave ends to wave backs, and as a result, a novel mechanism of self-supporting complicated spatio-temporal activity, unknown in reaction-diffusion population models.Comment: 15 pages, 15 figures, submitted to Chao