Narrow Results

In this paper, we investigate the dynamical behaviors of a modified Bazykin-type two predator-one prey model involving the intra-specific and inter-specific competition among predators. A Caputo fractional-order derivative is utilized to include the influence of the memory on the constructed mathematical model. The mathematical validity is ensured by showing the model always has a unique, non-negative and bounded solution. Four kinds of equilibria are well identified which represent the condition when all populations are extinct, both two predators are extinct, only the first predator is extinct, only the second predator is extinct, and all populations are extinct. The Matignon condition is given to identify the dynamics around equilibrium points. The Lyapunov direct method, the Lyapunov function, and the generalized LaSalle invariant principle are also provided to show the global stability condition of the model. To explore the dynamics of the model more deeply, we utilize the predictor–corrector numerical scheme. Numerically, we find the forward bifurcation and the bistability conditions by showing the bifurcation diagram, phase portraits, and the time series. The biological interpretation of the analytical and numerical results is described explicitly when an interesting phenomenon occurs.

Virtual knowledge brokers help their clients solve challenging innovation problems by leveraging the diverse knowledge basis of vast communities of solvers. Despite the increasing diffusion of virtual knowledge brokers, no efforts have been done so far to investigate the anatomy of the brokering process they follow to deliver a service to their clients. This paper analyses how virtual knowledge brokers go through the four macro-phases of the brokering process (i.e., access, learning, linking, and implementation) and points out the main differences with traditional brokers. The research is based on a multiple case study involving two Italian virtual knowledge brokers. The analysis suggests that virtual knowledge brokers are characterised by a stronger ability to access different knowledge domains in comparison with traditional knowledge brokers. However, virtual knowledge brokers are less effective in the learning and linking phases of the process, due to the distance that separates solvers and clients and the lack of communication and interaction between solvers. Starting from these insights, the ability of virtual and traditional knowledge brokers to solve different types of innovation problems is analysed. The paper contains also a discussion of the managerial implications of this study, especially for those firms that has to select the best knowledge brokers with which to collaborate.

The joint focus of TSG-46 on mathematics competitions and other challenging activities is devised in recognition of the fact that all students benefit from studying mathematics through challenging activities but some students do not like to compete. This group gathered mathematicians, teachers, mathematics educators and mathematics education researchers and served as a stage for presentations and discussions related to the following themes: (i) Organizational formats for challenging students mathematically, (ii) Research on students’ experiences with mathematically challenging activities, (iii) Characterizing and theorizing mathematical challenge, and (iv) Competition problems as impetus for mathematical research and discoveries.