In this paper, we propose a modified bursting neuron model, which is a natural extension of an original one proposed by the author et al. We will show that chaotic bursts appear in the modified model though there exhibit quasi-periodic bursts in the original one. Moreover, we will show that such chaotic bursts appear by breaking down a pair of invariant closed curves, which is generated by a Hopf bifurcation for a pair of two-periodic points.

In this paper, we consider a switching system modeled by a discrete-time flow model. By simulation, it is shown that a lot of border-collision bifurcations occur since the system is piecewise linear. By using its characteristics, we classify its dynamics into modes, and we define blocks and a kind of Poincare map based on the modes. We calculate occurrence conditions of each block and all the Poincare points by computer-assisted analysis. We consider two bifurcation phenomena, and we show that a Poincare point hits a boundary of the occurrence conditions of a block. So, both bifurcations are indeed border-collision bifurcations.

Over the past recent decades, numerous programming languages have expanded to embrace multi-paradigms such as the fusion of object-oriented and functional programming. For example, Java, one of the most famous object-oriented programming languages, introduced a number of functional idioms in 2014. This evolution enables developers to achieve various benefits from both paradigms. However, we do not know how Java developers use functional idioms actually. Additionally, the extent to which, while there are several criticisms against the idioms, the developers actually accept and/or use the idioms currently remains unclear. In this paper, we investigate the actual use status of three functional idioms (Lambda Expression, Stream, and Optional) in Java projects by mining 100 projects containing approximately 130,000 revisions. From the mining results, we determined that Lambda Expression is utilized in 16% of all the examined projects, whereas Stream and Optional are only utilized in 2% to 3% of those projects. It appears that most Java developers avoid using functional idioms just because of keeping compatibility Java versions, while a number of developers accept these idioms for reasons of readability and runtime performance improvements. Besides, when they adopt the idioms, Lambda Expression frequently consists of a single statement, and Stream is used to operate the elements of a collection. On the other hand, some developers implement Optional using deprecated methods. We can say that good usage of the idioms should be widely known among developers.