Key words relaxation oscillations, autoparametric, quenching, slow manifold. MSC (2000) 34C26, 34D15, 37N05, 70K70Stable normal mode vibrations in engineering can be undesirable and one of the possibilities for quenching these vibrations is by embedding the oscillator in an autoparametric system by coupling to a damped oscillator. We have the possibility of destabilising the undesirable vibrations by a suitable tuning and choice of coupling parameters. In the case of normal mode vibration derived from a relaxation oscillations we need low-frequency tuning of the attached oscillator. An additional feature is that to make the quenching effective we also have to deform the slow manifold by choosing appropriate coupling; this is illustrated for van der Pol relaxation. A number of numerical experiments have been done and show some interesting phenomena, such as a chaotic attractor and effective quenching.

This research focuses on the dynamical of a Leslie-Gower predator-prey model with competition on predator populations. The model represents an interaction between one prey and two predator populations. The analysis shows that there are four equilibrium points, namely the extinction of predator populations point, the extinction of the first predator population point, the extinction of the second predator and the interior point. The existence of the interior equilibrium point is investigated by using Cardan criteria. Local stability analysis shows that both predator populations have never been extinct together. The second and third equilibrium point is local asymptotically stable under some conditions. Numerical simulations are carried out to investigate the stability of the interior point as well as to show that more than one equilibrium point may be asymptotically stable together for a set of parameter.

This research involved 19 postgraduate students majoring on Science Education at one university in Surabaya who were programming Earth and Space Sciences course. The objective of this research is to measure students’ ability in designing a lesson plan for sustainable education on environmental issues around volcanoes by integrating education for sustainable development (ESD) competence. Descriptive quantitative analysis was employed to assess the lesson plans developed by the students. In general, the results showed that the lesson plans were less contextual to support the improvement of decision-making abilities on the environmental issues, the emergence of environmental awareness among students, encouragement to the students to have sense of belonging to the environment, and fostering critical analysis of various environmental phenomena. The results suggest further efforts to improve professional competence of the postgraduate students in developing geoscience learning instruments, particularly related to integrate the ESD competence into lesson plans.

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We study the dynamics of a modified Leslie–Gower one prey–two predators model with competition between predator populations. The model describes complex dynamics in the permanence, global stability and bifurcation. It is shown that there are eight possible equilibrium states. Two equilibrium states, i.e., the extinction of all of the species state and the extinction of both predators state are always unstable, while the other equilibrium states are conditionally locally and globally asymptotically stable. We also analyzed numerically the effect of competition between predators. Our numerical simulations showed that the competition rate of the second-predator may induce the transcritical bifurcation, the saddle-node bifurcation as well as the bi-stability phenomenon. Such numerical results are consistent with the analytical results.

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Numeracy is the ability to access, use, interpret and communicate information and mathematical ideas related to numbers in a particular context. Therefore numeracy skills are needed for a prospective elementary school teacher. The purpose of this research is to describes prospective elementary school teachers’ numeracy. This type of research is a qualitative descriptive study. This study’s subjects were prospective elementary school teachers’ from Universitas PGRI Adi Buana Surabaya, represented by one individual with low mathematical ability. Data were obtained through numeracy tasks. Prospective elementary school teachers with high ability can identify, find or access some mathematical information relevant to the purpose, involve using known mathematical procedures and rules, and develop opinions about that information. However, there are some errors in communicating according to the content based on its interpretation results. Prospective elementary school teachers with low ability have been able to identify, find or access some mathematical information relevant to the goal. Still, they have not been able to involve procedures and develop opinions about the information. Based on this study’s results, arithmetic needs to be a topic of attention to improve mathematics learning achievement in the future.