There is continuing debate about the space needs and requirements of broiler chickens, The aims of this study were to measure the amount of floor area a six-week-old broiler occupies for different behaviours and to use the obtained results in two models to estimate the number of birds that can be kept per m2 in large flocks simulating different levels of behavioural synchronisation. Photographs were taken of overhead projections of broilers (2.468 kg on average) kept in floor pens of 1 m2 with either eight (low density) or 16 birds (high density) per pen. Individual body space was measured from these photographs for seven behaviours. Posture and density affected body space of the behaviours idle, drinking, and ground pecking. The first model, computing space needed per bird performing a behaviour in relation to flock size, showed that 15.3-15.7 birds m−2 (37.8-38.7 kg m−2) can be housed maximally, based on low density measurements and 18.5-19.4 birds m−2 (45.7-47.9 kg m−2) based on high density measurements. The second model, computing stocking density based on synchronisation of behaviour and body space, showed that 13.7-15.9 birds m−2 (33.8-39.2 kg m−2) can be housed maximally based on low density measurements and 15.4-18.6 birds m−2 (38.0-45.9 kg m−2) based on high density measurements. Results based on high density measurements implied that birds are compressed. Given the restrictions of a limited number of behaviours and no inclusion of movement and social interactions in the models of this study, stocking density in large flocks should not exceed 16 birds m−2 (39.4 kg) because that would lead to compression of birds which will suppress opportunities for behavioural expression and therefore impair welfare.

Non-standard patterns of paid work are increasing in Australia, and young people are among the most affected. To investigate the impact of non-standard work schedules on young people’s relationships, this article draws on data from 50 interviews conducted in 2008 and 4 surveys conducted between 2007 and 2012 with 636 young people (aged 18–24 years), all participating in the Life Patterns Project longitudinal study of youth in Australia. Over the 6 years, a majority of participants were engaged in non-standard work, working weekends, evenings or public holidays. A significant minority also faced weekly variability in their work schedules. The interview data suggest that these patterns of employment can be considered unsocial, making it more difficult to find regular periods of time together with a group of friends. Interview discussion also suggests that as a substitute for a greater quantity of shared time, some young people seek out shared experiences felt to be intense or out of the ordinary, such as that facilitated by alcohol consumption, to make the most of limited opportunities to bond with a group of close friends.

We introduce a general two-colour interacting urn model on a finite directed graph, where each urn at a node reinforces all the urns in its out-neighbours according to a fixed, non-negative, and balanced reinforcement matrix. We show that the fraction of balls of either colour converges almost surely to a deterministic limit if either the reinforcement is not of Pólya type or the graph is such that every vertex with non-zero in-degree can be reached from some vertex with zero in-degree. We also obtain joint central limit theorems with appropriate scalings. Furthermore, in the remaining case when there are no vertices with zero in-degree and the reinforcement is of Pólya type, we restrict our analysis to a regular graph and show that the fraction of balls of either colour converges almost surely to a finite random limit, which is the same across all the urns.

Neural mass models are ubiquitous in large-scale brain modelling. At the node level, they are written in terms of a set of ordinary differential equations with a non-linearity that is typically a sigmoidal shape. Using structural data from brain atlases, they may be connected into a network to investigate the emergence of functional dynamic states, such as synchrony. With the simple restriction of the classic sigmoidal non-linearity to a piecewise linear caricature, we show that the famous Wilson–Cowan neural mass model can be explicitly analysed at both the node and network level. The construction of periodic orbits at the node level is achieved by patching together matrix exponential solutions, and stability is determined using Floquet theory. For networks with interactions described by circulant matrices, we show that the stability of the synchronous state can be determined in terms of a low-dimensional Floquet problem parameterised by the eigenvalues of the interaction matrix. Moreover, this network Floquet problem is readily solved using linear algebra to predict the onset of spatio-temporal network patterns arising from a synchronous instability. We further consider the case of a discontinuous choice for the node non-linearity, namely the replacement of the sigmoid by a Heaviside non-linearity. This gives rise to a continuous-time switching network. At the node level, this allows for the existence of unstable sliding periodic orbits, which we explicitly construct. The stability of a periodic orbit is now treated with a modification of Floquet theory to treat the evolution of small perturbations through switching manifolds via the use of saltation matrices. At the network level, the stability analysis of the synchronous state is considerably more challenging. Here, we report on the use of ideas originally developed for the study of Glass networks to treat the stability of periodic network states in neural mass models with discontinuous interactions.

The master stability function is a powerful tool for determining synchrony in high-dimensional networks of coupled limit cycle oscillators. In part, this approach relies on the analysis of a low-dimensional variational equation around a periodic orbit. For smooth dynamical systems, this orbit is not generically available in closed form. However, many models in physics, engineering and biology admit to non-smooth piece-wise linear caricatures, for which it is possible to construct periodic orbits without recourse to numerical evolution of trajectories. A classic example is the McKean model of an excitable system that has been extensively studied in the mathematical neuroscience community. Understandably, the master stability function cannot be immediately applied to networks of such non-smooth elements. Here, we show how to extend the master stability function to non-smooth planar piece-wise linear systems, and in the process demonstrate that considerable insight into network dynamics can be obtained. In illustration, we highlight an inverse period-doubling route to synchrony, under variation in coupling strength, in globally linearly coupled networks for which the node dynamics is poised near a homoclinic bifurcation. Moreover, for a star graph, we establish a mechanism for achieving so-called remote synchronisation (where the hub oscillator does not synchronise with the rest of the network), even when all the oscillators are identical. We contrast this with node dynamics close to a non-smooth Andronov–Hopf bifurcation and also a saddle node bifurcation of limit cycles, for which no such bifurcation of synchrony occurs.

Many couples want to retire together even if spouses differ in age. Drawing on theories of leisure complementarity, gender roles and social status, this article uses comprehensive Swedish register data from 2002 to 2010 to explore synchronised retirement and its association with spousal age differences and other socio-demographic factors. Synchronisation rates in dual-earner couples (N = 83,986) were 10 per cent for retirement the same calendar year and 25 per cent for retirement the same or the following year. Contrary to theoretical expectations, synchronisation was more common in women-older couples than in men-older couples, although this was largely a consequence of the skewed distribution of age differences. Moreover, spouses' education, incomes, assets, employment and health were differently associated with synchronisation in same-age, men-older and women-older couples. In the total population, average retirement age differed very little between synchronising couples and other couples. Yet women who synchronised retired at an earlier age than other women, whereas men who synchronised retired later than other men. This was partly an effect of the predominance of men-older couples, but men in men-older couples were also more likely than women in women-older couples to delay retirement in order to synchronise.

Synchronisation is one of the most interesting collective motions observed in large-scale complex networks of interacting dynamical systems. We consider global synchronisation for networks of nonlinearly coupled identical cells with time delays, using an approach where the synchronisation problem is converted to solving an homogeneous linear system. This approach is extended to fit networks under more general coupling topologies, and we derive four delay-dependent and delay-independent criteria that ensure the coupled dynamical network is globally synchronised. Some examples show that the four criteria are not mutually inclusive, and numerical simulations also demonstrate our theoretical results.

Important developments have occurred in the last two decades, since the advent of the Ovsynch protocol, on the understanding and use of synchronisation programmes for management of reproduction in dairy herds. This better understanding of oestrus cycle control associated with suboptimal reproductive performance in dairy herds has led dairy producers to quickly adopt timed artificial insemination (AI) protocols. Recent surveys have documented that fixed-time AI has become an important component of management of reproduction in high-producing herds. Furthermore, timed AI protocols have also demonstrated benefits in pasture-based milk production systems because of the ability to increase insemination rate. In general, successful use of the Ovsynch protocol requires some fundamental physiological principles to be respected, including: induction of ovulation to synchronise follicle growth in the first 2 days of the programme such that a young antral follicle is recruited; maintenance of high concentrations of progesterone during the development of the ovulatory follicle, but also effectively lyse the corpus luteum to result in very low concentration of progesterone at AI; and having a healthy pre-ovulatory follicle of moderate diameter that is highly oestrogenic and responsive to gonadotropins to synchronously ovulate 12 to 18 h after insemination. Current methods oestrous and ovulation synchronisation are still not optimal and future improvements will likely require new technologies for hormone formulation and delivery such that additional interventions are minimised to maintain acceptance by producers.

An emerging research topic in civil engineering is the dynamic interaction between crowdsand structures. Structures such as footbridges, which oscillate due to the crossing of agroup of pedestrians, or stands within stadia or concert halls, which vibrate due to therythmic movement of the audience are of particular interest. The objective of this studyis twofold: modelling the movement of pedestrians with consideration ofpedestrian-pedestrian, and pedestrian-obstacle interactions, and the incorporation of apedestrian-structure coupling in the previous model. Frémond’s model, which allows us tosimulate the movement of an assembly of particles and accounts for collisions amongconsidered rigid particles, is presented and adapted to the crowd by giving a willingnessto the circular particles, which allows each pedestrian to move according to a giventarget. To handle the crowd-structure interaction in the case of lateral oscillations offootbridges, the Kuramoto differential equation governing the time evolution of thelateral motion of each pedestrian is implemented in the previous model. Preliminaryresults obtained from numerical simulations are presented and discussed.