Global attractors, extremal stability and periodicity for a delayed population model with survival rate on time scales.

In this paper, we investigate the existence of global attractors, extreme stability, periodicity and asymptotically periodicity of solutions of the delayed population model with survival rate on isolated time scales given by $ x^{\Delta} (t) = \gamma(t) x(t) + \dfrac{x(d(t))}{\mu(t)}e^{r(t)\mu(t)\left(1 - \frac{x(d(t))}{\mu(t)}\right)}, \ \ t \in \mathbb T. $ We present many examples to illustrate our results, considering different time scales.

Black globe temperature from meteorological data and a bioclimatic analysis of the Brazilian Northeast for Saanen goats.

The black globe temperature (BGT) is not a common measurement for weather station networks, despite having great relevance to bioclimatic studies. The aim of this study was to propose equations for estimating the BGT, using meteorological data for different time scales and a bioclimatic evaluation of the Brazilian Northeast for breeding Saanen dairy goats. The data used in elaborating the equations were collected between 1 November 2014 and 31 October 2017. Data for BGT, incident global solar radiation (SR), air temperature (AT), relative humidity (RH) and wind speed were handled on a daytime, night-time, daily and monthly scale. One half of the database was used to adjust the equations and the other half in the evaluation. The bioclimatic diagnosis of the Brazilian Northeast was carried out based on mean monthly values of the black globe temperature and humidity index (BGHI) estimated for the four seasons of the year. For the daytime scale, an equation based on AT (BGT = 1.3897.AT-5.4421, r2 = 0.80) and a multiplicative model combining the effects of AT and SR (BGT = [1.3897.AT-5.4421] (0.0384.ln(SR)+0.7935], r2 = 0.91) were obtained. AT adjusted well for BGT on the night-time scale (BGT = 0.995.AT-0.6964, r2 = 0.99), daily scale (BGT = 1.1641.AT-1.5941, r2 = 0.97) and monthly scale (BGT = 1.1550.AT-1.3498, r2 = 0.98). The BGT can therefore be calculated from AT and/or SR for the daytime scale, and from AT only for the night-time, daily and monthly scales. In general, the west and centre-south of the state of Bahia offer the animals the most thermal comfort during each season of the year. In the state of Maranhão, heat stress occurs throughout the year, with the BGTI predominately in the range of 85-95. As such, strategies to combat heat stress should be encouraged to minimise the negative effects of climate on milk production in Saanen goats, and favour the milk-production chain in the northeast of Brazil.

Membrane potential resonance in non-oscillatory neurons interacts with synaptic connectivity to produce network oscillations.

Several neuron types have been shown to exhibit (subthreshold) membrane potential resonance (MPR), defined as the occurrence of a peak in their voltage amplitude response to oscillatory input currents at a preferred (resonant) frequency. MPR has been investigated both experimentally and theoretically. However, whether MPR is simply an epiphenomenon or it plays a functional role for the generation of neuronal network oscillations and how the latent time scales present in individual, non-oscillatory cells affect the properties of the oscillatory networks in which they are embedded are open questions. We address these issues by investigating a minimal network model consisting of (i) a non-oscillatory linear resonator (band-pass filter) with 2D dynamics, (ii) a passive cell (low-pass filter) with 1D linear dynamics, and (iii) nonlinear graded synaptic connections (excitatory or inhibitory) with instantaneous dynamics. We demonstrate that (i) the network oscillations crucially depend on the presence of MPR in the resonator, (ii) they are amplified by the network connectivity, (iii) they develop relaxation oscillations for high enough levels of mutual inhibition/excitation, and (iv) the network frequency monotonically depends on the resonators resonant frequency. We explain these phenomena using a reduced adapted version of the classical phase-plane analysis that helps uncovering the type of effective network nonlinearities that contribute to the generation of network oscillations. We extend our results to networks having cells with 2D dynamics. Our results have direct implications for network models of firing rate type and other biological oscillatory networks (e.g, biochemical, genetic).

Hydrodynamic modelling of a polluted tropical bay: Assessment of anthropogenic impacts on freshwater runoff and estuarine water renewal.

A bay's capacity to buffer fluvial fluxes between the land and sea is sensitive to hydrological changes that can affect its water renewal rates. In Cartagena Bay, Colombia, pollution issues have been associated with freshwater fluxes which are projected to increase in future years. This has led to plans to reduce freshwater flows by constructing upstream hydraulic doors. Given the influence of freshwater discharge on coastal water renewal, it is important to assess how these upstream changes will affect the bay's hydrodynamic processes. This study calibrated the 3D MOHID Water model, configured with a high-resolution mixed vertical discretization to capture the bay's characteristic processes of vertical stratification and mixing. A Lagrangian transport model was used to analyze the flow of passive particle tracers and calculate water renewal time scales. Mean residence times of 3-6 days and flushing times of 10-20 days for canal water were found, while mean residence times of 23-33 days and flushing times of 70-99 days were calculated for the bay's complete water volume. An assessment of future scenarios showed that increases in freshwater runoff would result in faster water renewal in the bay, while plans to decrease freshwater discharge would result in slower water renewal in the bay. It is therefore imperative that any plans for reducing fluvial fluxes into the bay be accompanied by the control of local pollution sources, which are abundant and could worsen the bay's water quality issues should water renewal times become longer.