Judul: Bifurkasi lokal pada titik tetap non-hiperbolik
Abstrak: Bifurkasi menggambarkan perubahan pada struktur orbit di sekitar titik tetap. Titik tetap dibagi menjadi dua yaitu titik tetap hiperbolik dan titik tetap non-hiperbolik. Titik tetap non-hiperbolik terjadi jika ada nilai eigen dengan bagian real sama dengan nol. Kestabilan dari titik tetap dapat diketahui dari nilai eigen yang diperoleh dari pelinearan medan vektor. Pada bifurkasi satu-dimensi ditemukan kasus-kasus untuk bifurkasi saddle-node, bifurkasi transcritical dan bifurkasi pitchfork. Bifurkasi saddle-node terjadi jika satu sisi dari nilai parameter tidak terdapat titik tetap dan pada sisi lain terdapat dua titik tetap, dimana yang satu stabil dan yang lainnya tak-stabil. Bifurkasi transcritical terjadi jika terdapat pertukaran kestabilan, yaitu dari titik tetap stabil menjadi titik tetap tak-stabil dan sebaliknya. Sedangkan bifurkasi pitchfork dibagi menjadi dua, yaitu: bifurkasi pitchfork supercritical dan bifurkasi pitchfork subcritical. Bifurkasi pitchfork supercritical terjadi jika satu titik tetap stabil berubah menjadi dua titik tetap stabil dan satu titik tetap tak-stabil, dan bifurkasi pitchfork subcritical terjadi jika satu titik tetap stabil dan dua titik tetap tak-stabil berubah menjadi satu titik tetap tak-stabil. Bifurkasi Hopf (bifurkasi dua-dimensi) terjadi jika terdapat orbit periodik pada struktur orbitnya yang berupa lingkaran dengan jari-jari konstan. Ada atau tidaknya orbit periodik dapat diketahui setelah sistem ditransformasikan ke dalam koordinat polar. Orbit periodik ini dapat bersifat stabil maupun tak-stabil. Model periklanan (advertising) Feichtinger merupakan salah satu contoh penerapan bifurkasi Hopf Model ini menghasilkan satu titik tetap dan orbit periodik yang bersifat stabil.
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Judul: Bifurkasi pada Model Interaksi Tumbuhan dan Herbivora
Abstrak: Saha dan Bandyopadhyay (2005) memodelkan sistem mangsa-pemangsa yang merepresentasikan interaksi tumbuhan dan herbivora. Pada karya ilmiah ini, dicari bifurkasi yang terjadi dengan terlebih dulu menganalisis kestabilan titik tetap. Ada tiga titik tetap yang diperoleh dengan jenis kestabilan titik tetap ditentukan oleh nilai eigen yang diperoleh dari ketiga titik tetap tersebut. Titik tetap pertama dan kedua bersifat sadel dan terdapat empat kasus pada titik tetap ketiga agar mencapai kestabilan. Dengan pemilihan parameter tertentu, diperoleh bifurkasi Hopf yakni terjadinya perubahan kestabilan dari spiral stabil menjadi spiral tak stabil dan terdapat limit cycle pada titik tetap ketiga.
Keyword: bifurkasi Hopf, limit cycle, model interaksi tumbuhan dan herbivora

Judul: Drought Stress Tolerance Mechanisms of Eggplant (Solanum spp.): Physiology and Molecular.
Abstrak: Eggplant (Solanum melongena L.) is a popular and economically important vegetable crop grown in the tropics and subtropics, especially in Asia and Africa. Most of these crops grown in Asia and Africa are tolerant to biotic and abiotic stresses. Eggplant has a wide variation in morphological and physiological characteristics, therefore, it is necessary to explore the germplasm to gain more genotypes tolerant to biotic and abiotic stresses. Sufficient water availability at the first stage of plant growth is very important. Limited water supply may lead to drought stress. The long period of drought stress may disturb the metabolic process and lead the irreversible damage of the plant tissues, so the plant can not recover. This abiotic stress has been significantly proved to be one of factors decreasing the plant growth and productivity. The objective of this research was to reveal physiological and molecular response of six eggplant accessions (i.e. 098, 155, 414, 754, 772, and 827 accessions, and Panjalu-F1 as the control genotype) to drought stress. Plants were grown in medium containing soil, sand and compost (1:1:1, v/v/v) in the greenhouse. Plants were exposed to the drought treatment at 21 days after the plants have 6 fully leaves. Some parameters were examined during the drought treatment, which were media water content (MWC), relative water content (RWC), plant growth and dry weight, proline concentration, chlorophyll content and polyamine concentration. Total RNA was extracted from leaves on day 21st of the treatment. The arginine decarboxylase S. melongena (SmADC) fragment gene was amplified from the cDNA. ADC gene is one of genes involved in polyamine biosynthesis and plays important role in the plant tolerance mechanism to drought stress. The results showed that drought stress significantly reduced plant height, leaf area, stomatal density and aperture in all plants. Levels of chlorophylls were similar during the drought treatment in all plants. Proline and/or polyamines were accumulated and reached the maximum levels after 14 to 21 days after the treatment. High levels of these amines can be used to indicate that the plant is stressed by drought. Levels of proline and polyamines, especially putrescine, increased 10 times higher in the stressed-plants compared to those grown in the optimum condition. cDNA was synthesized from the total RNA by reverse transcription. In total, four fragments of SmADC were obtained by PCR from cDNA of accession 098 (2 fragments), cDNA of accession 772 (1 fragment) and genomic DNA of accession 098 (1 fragment). ADC primers were designed based on the conserved regions in ADC Solanum lycopersicum (accession number HM629957.1). Sequences analysis showed that the four SmADC fragments were 1 442 bp, 1 422 bp, 1 407 bp and 636 bp, encoding 151, 357, 466, 182 amino acids, respectively. Nucleotide alignment analysis showed that four SmADC fragments were 86-93 % homologue to Solanum lycopersicum (Acc: NM_001247720.1), Datura stramonium (Acc: AJ251898.1), Capsicum annuum (Acc: AY156514.1) and Nicotiana tabacum (Acc: AF321137.1). Based on the phylogenetic tree developed from the deduced amino acid sequence of ADC, SmADCs were grouped with Solanum lycopersicum, Datura stramonium, Capsicum annuum and Nicotiana tabacum. Analysis of conserved domains revealed that
Keyword: eggplant, proline, polyamine, arginine decarboxylase (ADC), pyridoxal 5-phosphate (PLP)