Scaling law in Saddle-node bifurcations for one-dimensional maps: A complex variable approach

The study of transient dynamical phenomena near bifurcation thresholds has attracted the interest of many researchers due to the relevance of bifurcations in different physical or biological systems. In the context of saddle-node bifurcations, where two or more fixed points collide annihilating each other, it is known that the dynamics can suffer the so-called delayed transition. This phenomenon emerges when the system spends a lot of time before reaching the remaining stable equilibrium, found after the bifurcation, because of the presence of a saddle-remnant in phase space. Some works have analytically tackled this phenomenon, especially in time-continuous dynamical systems, showing that the time delay, tau, scales according to an inverse square-root power law, tau similar to (mu-mu (c) )(-1/2), as the bifurcation parameter mu, is driven further away from its critical value, mu (c) . In this work, we first characterize analytically this scaling law using complex variable techniques for a family of one-dimensional maps, called the normal form for the saddle-node bifurcation. We then apply our general analytic results to a single-species ecological model with harvesting given by a unimodal map, characterizing the delayed transition and the scaling law arising due to the constant of harvesting. For both analyzed systems, we show that the numerical results are in perfect agreement with the analytical solutions we are providing. The procedure presented in this work can be used to characterize the scaling laws of one-dimensional discrete dynamical systems with saddle-node bifurcations.

PBL in healthcare sciences: a case study on curriculum innovation

Students of a Cardiopulmonary Sciences curriculum in a Portuguese higher education institution have shown poor learning outcomes and low satisfaction on a course about lung function tests. A transmissive pedagogical approach, mainly based on lectures, was the common teaching practice. Aiming for a change, PBL was considered as a powerful alternative and also as a contribution for progressively innovating the curriculum. Purpose: to create PBL activities in a lung function tests course. to describe their implementation, to analyse the effects of PBL integration in students’ performance and attitudes, to characterize the generated learning environment.

Risk assessment in open innovation networks

Innovation is considered crucial for enterprises survival and current economic environment demands the best ways of achieving it. However, the development of complex products and services require the utilization of diverse know-how and technology, which enterprises may not hold. An effective strategy for achieving them is to rely in open innovation. Still, open innovation projects may fail for many causes, e.g. due to the dynamics of collaboration between partners. To effectively benefit from open innovation, it is recommended the utilization of adequate risk models. For achieving such models, a preliminary conceptualization of open innovation and risk is necessary, which includes modeling experiments with existing risk models, such as the FMEA.

Innovation from Academia-Industry symbiosis

Anchored on a systemic perspective of innovation and particularly on the triple helix model, which highlights the state, university and companies as central players, this paper aims to discuss the factors that enable or constrain the processes of innovation, using the system thinking approach to understand the academia-industry symbiosis. The paper's empirical section is based on a case study on Portugal's major highway management concessionaire. In order to ensure a "healthy" co-innovation environment, the archetype studied emphasizes the need to implement coordination mechanisms such as communication routines and metrics to monitor collaborative behavior in addition to the need to develop global goals that align the efforts of the partners.