Judul: Bifurkasi Hopf Pada Model Mangsa-Pemangsa Tipe Leslie Dengan Fungsi Respons Holling Tipe Iii
Abstrak: Mangsa-Pemangsa Merupakan Salah Satu Fenomena Alam Yang Dipelajari Untuk Studi Dampak Keseimbangan Alam Yang Diakibatkan Oleh Dua Spesies Yang Berinteraksi. Terdapat Beberapa Model Matematis Untuk Memodelkan Peristiwa Mangsa-Pemangsa. Dalam Karya Ilmiah Ini Direkonstruksi Model Mangsa-Pemangsa Tipe Leslie Dengan Fungsi Respons Holling Tipe Iii. Simulasi Dilakukan Untuk Melihat Pengaruh Parameter Terhadap Kestabilan Sistem. Dengan Memilih Nilai Parameter Yang Tepat, Diperoleh Satu Sampai Dengan Empat Titik Tetap. Dinamika Populasi Mangsa-Pemangsa Pada Model Ini Dibagi Menjadi Empat Kasus. Pada Kasus Kedua, Terjadi Perubahan Kestabilan Titik Tetap Dari Spiral Stabil Menjadi Spiral Takstabil, Disertai Adanya Kemunculan Limit Cycle. Kemunculan Limit Cycle Tersebut Menandakan Terjadi Bifurkasi Hopf
Keyword: bifurkasi Hopf, Holling tipe III, limit cycle, mangsa-pemangsa

Judul: Bifurkasi Hopf pada Model Mangsa-Pemangsa Holling-Tanner Tipe II
Abstrak: In this paper a mathematical prey-predator model of Holling-Tanner type II and the existence of Hopf bifurcation were studied. In this model, three fixed points are obtained, in which one of them is a saddle point. The prey-predator population dynamics was simulated based on four cases, by increasing the interaction value of prey and predator. In the third case, the stable spiral changed into an unstable spiral and also observed the presence of limit cycles. This is known as Hopf bifurcation. Furthermore, for the fourth case both populations were almost extincted due to the increase of the interaction rate. Generally, it can be concluded that increasing the value of prey and predator interaction rate would change the stability of population. The prey-predator population will be stable when the prey and predator interaction rate is low, whereas the higher interaction rate would cause the extinction of both prey and predator populations
Keyword: prey-predator., limit cycle, Holling-Tanner type II, Hopf bifurcation

Judul: Characteristic of chili drying (Capsicum annum L.) as a natural dyeing cosmetic
Abstrak: Chilli (Capsicum sp.) contains carotenoids, which are a group of natural pigments consist of red, orange or yellow color. Carotenoids can be dissolved in lipid so that they can be applied to oil-based cosmetic ingredients. Therefore, chilli is potential to be developed as cosmetic colorants. However, pungency of red chili needs to be removed because it is irritating and it provides stinging sensation to skin. Red chilli was investigated as a potent material for a cosmetic colourant in this research because it has a nice uniform red color and has a pungency level less than cayenne pepper. The purpose of this research was to investigate the influence of blanching on drying characteristics of red chilli using a tray dryer, determine the proper time of chili blanching in sodium bisulfite solution, examine color changes stability of red chili powder as a cosmetic dye, and analyze the effect of oleoresin extraction on color and pungency level of red chili powder. The results showed that blanching could affect the drying characteristics. Blanching the chilli for 9 minutes prior drying could speed up the drying rate of chilli and thus the drying time, therefore, the chilli achieved the desired moisture content fast. Sodium bisulfite solution of 0.2%, used as the blanching media, could maintain the color well. However, longer time of blanching might cause several pigments soluble in the blanching media. Blanching the chilli for 9 minutes was able to maintain red color after the stability tested and after extraction of oleoresin. Therefore, blanching red chilli in a solution of 0.2% sodium bisulfite for 9 minutes prior drying is concluded as the best treatment to retain the color of red chilli powder
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