Article Per Year (5 Year)
p-Index From 2020 - 2025
0.444
P-Index
This Author published in this journals
All Journal Jurnal Sains Dasar Jurnal Pengabdian Masyarakat MIPA dan Pendidikan MIPA Jurnal Kajian dan Terapan Matematika
Kus Prihantoso Krisnawan
Jurusan Pendidikan Matematika, FMIPA, Universitas Negeri Yogyakarta
Computer Science & IT Decision Sciences, Operations Research & Management Education Mathematics

Published : 10 Documents Claim Missing Document
Claim Missing Document
Check
Articles

Found 10 Documents
Search

 1 
Identifikasi bifurkasi kodimensi-2 pada sistem flutter dengan menggunakan kriteria Routh Hartono, Hartono; Krisnawan, Kus Prihantoso
Jurnal Sains Dasar Vol 3, No 1 (2014): April 2014
Publisher : Faculty of Mathematics and Natural Science, Universitas Negeri Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (290.032 KB) | DOI: 10.21831/jsd.v3i1.2779

Abstract

In this paper, the codimension-2 bifurcation of a 2-parameter flutter system is identified using Routh’s criterion. Routh’s criterion is a tool to determine the number of roots of a real polynomial in the right half-plane. Based on this criterion, the regions borders of each parameter are determined in order to make the roots of flutter system characteristic equation have negative or positive real parts. A point is taken from each region and the phase portraits of the system are drawn. Based on the Routh’s table and the phase portraits, different dynamical structure that showing a pitchfork-hopf bifurcation is acquired. Key words: pitchfork-hopf bifurcation, flutter system, Routh’s criterion
PARALLEL COORDINATE APPLICATION IN 4 DIMENSION ROOM AT PLANE TRAFFIC DISPLAY Hartono, Hartono; Krisnawan, Kus Prihantoso; Arifah, Husna
Jurnal Sains Dasar Vol 4, No 2 (2015): Jurnal Sains Dasar
Publisher : Yogyakarta State University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (41.588 KB)

Abstract

This research aims to describe ann-dimensional line on a parallel coordinate and uses the representation as a display of aircraft motion which flies at a straight line and constant velocity. A parallel coordinate of n-dimensional space depicted in the form of nparallel vertical lines which represent axis.Every two adjacent axes have the same distance. A horizontal line that cutsall axes indicates the initial pointsof each axis. In a parallel coordinate,an 15n"> -dimensional point is represented as a polygonal chainwhere the vertices located on its axis. Based on the representations of some of collinear points, a line is described on a parallel coordinate. On the other hand, one can consider a graph of an aircraft motion as a graph of a 4-dimensional space. At a constant speed with a straight line orbit, the graph of an aircraft movementis a graph of 4-dimensional line. The result shows that, on a parallel coordinate, an n-dimensional line represented as 15n-1">  dots. As a consequence, the graph of an aircraft that moveat a constant speed with a straight line orbitrepresented as3 dots. By this representation, the coordinate and altitude of the aircraft can be observes at anytime. It also shows whether the movement of an aircraft disturb (strike or too close to) another plane or not. Keywords: parallel coordinate, n-dimensional space, aircraft movement display
APLIKASI KOORDINAT PARALEL DI DALAM RUANG DIMENSI 4 PADA DISPLAY LALU-LINTAS PESAWAT Hartono Hartono; Kus Prihantoso Krisnawan; Husna Arifah
Jurnal Sains Dasar Vol 4, No 2 (2015): October 2015
Publisher : Faculty of Mathematics and Natural Science, Universitas Negeri Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21831/jsd.v4i2.9814

Abstract

This research aims to describe ann-dimensional line on a parallel coordinate and uses the representation as a display of aircraft motion which flies at a straight line and constant velocity. A parallel coordinate of n-dimensional space depicted in the form of nparallel vertical lines which represent axis.Every two adjacent axes have the same distance. A horizontal line that cutsall axes indicates the initial pointsof each axis. In a parallel coordinate,an 15n" -dimensional point is represented as a polygonal chainwhere the vertices located on its axis. Based on the representations of some of collinear points, a line is described on a parallel coordinate. On the other hand, one can consider a graph of an aircraft motion as a graph of a 4-dimensional space. At a constant speed with a straight line orbit, the graph of an aircraft movementis a graph of 4-dimensional line. The result shows that, on a parallel coordinate, an n-dimensional line represented as 15n-1"  dots. As a consequence, the graph of an aircraft that moveat a constant speed with a straight line orbitrepresented as3 dots. By this representation, the coordinate and altitude of the aircraft can be observes at anytime. It also shows whether the movement of an aircraft disturb (strike or too close to) another plane or not. Keywords: parallel coordinate, n-dimensional space, aircraft movement display
On the othogonal trajectories and conformal mapping of complex variable functions Kus Prihantoso Krisnawan; Atmini Dhoruri
Jurnal Sains Dasar Vol 3, No 2 (2014): October 2014
Publisher : Faculty of Mathematics and Natural Science, Universitas Negeri Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (311.404 KB) | DOI: 10.21831/jsd.v3i2.4110

Abstract

This research goal is to investigate the connection of orthogonal trajectories, analitic functions, and conformal mapping. Orthogonal trajectories are the intersection of two families of mutually perpendicular curves. The analytical property of a complex function f(z) = u + iv is investigated using Cauchy-Riemann conditions and then the geometric shapes of u and v are interpreted. The results showed that if two functions are mutually harmonic conjugate, then they are mutually orthogonal trajectories. If two families of curves of mutually orthogonal trajectories are mapped by conformal mapping then the result functions are also mutually orthogonal trajectories.Key words: orthogonal trajectories, analytic functions, conformal mapping
THE EFFECT OF NONLINEAR DAMPING TO A DYNAMICAL SYSTEM WITH CENTER PHASE PORTRAIT Kus Prihantoso Krisnawan; Husna Arifah
Jurnal Sains Dasar Vol 4, No 1 (2015): April 2015
Publisher : Faculty of Mathematics and Natural Science, Universitas Negeri Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21831/jsd.v4i1.8439

Abstract

This paper discusses the effect of nonlinear damping to a 2-dimesional system that has center phase portrait. The phase portraits of the damped system are drawn for 3 different values of parameter. These phase portraits stand as the numerical proof of phase portrait change. To prove the change analiticaly, we use the theorem that guarantee the existence of periodic solution. The result shows that nonlinear damping changes the phase portrait topologically. It means that the system undergoes a generalized Hopf bifurcation. Keywords: generalized Hopf bifurcation, center phase portrait, periodic solution
Bifurkasi pitchfork pada sistem flutter sayap pesawat terbang Hartono '; Kus Prihantoso Krisnawan
Jurnal Sains Dasar Vol 2, No 2 (2013): October 2013
Publisher : Faculty of Mathematics and Natural Science, Universitas Negeri Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21831/jsd.v2i2.3295

Abstract

  Abstrak Penelitian ini bertujuan untuk menganalisis terjadinya bifurkasi pada sistem flutter. Sistem flutter merupakan model matematika dari fenomena ketidakstabilan dinamik yang terjadi pada struktur fleksibel pesawat terbang karena adanya gaya aerodinamis yang ditambahkan. Analisis dilakukan dengan cara mentransformasi sistem berdasarkan teori center manifold sehingga didapatkan bentuk normal suatu bifurkasi. Hasil analisis menunjukkan bahwa pada sistem flutter terjadi bifurkasi pitchfork. Kata kunci: bifurkasi pitchfork, sistem flutter, center manifold  
Peningkatan Profesionalisme Guru Matematika SMK Se-Gunungkidul Melalui Workshop Pemodelan Matematika Himmawati Puji Lestari; Hartono Hartono; Nikenasih Binatari; Emut Emut; Fitriana Yuli Saptaningtyas; Kus Prihantoso Krisnawan
Jurnal Pengabdian Masyarakat MIPA dan Pendidikan MIPA Vol 4, No 1 (2020): Vol 4, no 1 (2020)
Publisher : Yogyakarta State University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (288.467 KB) | DOI: 10.21831/jpmmp.v4i1.34079

Abstract

AbstrakParadigma pembelajaran di sekolah menengah kejuruan sebaiknya mempertimbangkan kebutuhan dunia kerja, mengacu pada standar kompetensi dunia kerja atau dunia industri misalnya kemampuan pemecahan masalah dan kemampuan berpikir kritis. Kemampuan ini dapat ditumbuhkembangkan melalui pembelajaran matematika, khususnya pemodelan matematika. Oleh karena itu, tim pengabdi memandang perlu dilakukannya sebuah workshop untuk mewadahi guru-guru SMK dalam meningkatkan penguasaan materi tentang pemodelan matematika. Program Pengabdian Masyarakat ini, diselenggarakan dalam bentuk workshop selama 2 hari untuk (1) Menjelaskan tentang Pemodelan Matematika, (2) Menyusun model matematika dari masalah kontekstual / soal aplikasi, (3) Menyelesaikan masalah kontekstual / soal aplikasi dan (4) Media pembelajaran berbasis teknologi informasi yang dapat membantu menyelesaikan masalah kontekstual / soal aplikasi. Berdasarkan evaluasi diperoleh beberapa hal sebagai berikut: 1) Kegiatan PPM workhop Pemodelan Matematika ini telah dilaksanakan dan berjalan dengan baik dan lancar; 2) Peserta mengikuti workshop dengan antusias dan memandang bahwa kegiatan ini perlu diselenggarakan; 3) Berdasarkan hasil evaluasi dari angket, pelaksanaan kegiatan workshop ini berjalan sangat baik dengan skor 4.29 dari skor maksimum 500; 4) Berdasarkan tes kemampuan pemodelan matematika, diperoleh peserta memperoleh skor rerata 7,85 dari skor maksimum 10. Kata kunci: workshop, pemodelan matematika, Geogebra, Tora Improving Professionalism of Mathematics Teacher In Gunungkidul Vocational Schools Through Mathematics Modelling WorkshopAbstractThe learning paradigm in vocational high schools should consider the needs of the world of work, referring to the competency standards of the world of work or industry such as problem solving skills and critical thinking skills. This ability can be developed through learning mathematics, especially mathematical modeling. Therefore, the service team deems it necessary to hold a workshop to facilitate vocational teachers in increasing mastery of material on mathematical modeling. This Community Service Program, held in the form of a workshop for 2 days to (1) Explain about Mathematical Modeling, (2) Develop mathematical models of contextual problems / application problems, (3) Solve contextual problems / application problems and (4) Learning media based information technology that can help solve contextual problems / application problems. Based on the evaluation, several things are obtained as follows: 1) The PPM Mathematics Modeling workhop activity has been carried out and runs well and smoothly; 2) Participants attend the workshop enthusiastically and view that this activity needs to be held; 3) Based on the evaluation results from the questionnaire, the implementation of the workshop activities went very well with a score of 4.29 from a maximum score of 500; 4) Based on tests of mathematical modeling abilities, the participants obtained an average score of 7.85 from a maximum score of 10. Key words: workshop, mathematical modelling, Geogebra, TORA
ANALISIS KESTABILAN MODEL MATEMATIKA PENGARUH VAKSINASI TERHADAP KASUS POSITIF COVID-19 DI PROVINSI DAERAH ISTIMEWA YOGYAKARTA Wiwit Wahyuningsih; Kus Prihantoso Krisnawan
Jurnal Kajian dan Terapan Matematika Vol 9, No 1 (2023): Jurnal Kajian dan Terapan Matematika (Maret)
Publisher : Jurnal Kajian dan Terapan Matematika

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Tujuan penelitian ini adalah menjelaskan pengaruh vaksinasi terhadap kasus positif Covid–19 di Provinsi Daerah Istimewa Yogyakarta menggunakan pemodelan matematika, menjelaskan kestabilan titik ekuilibrium, dan menjelaskan solusi numerik. Model yang digunakan yaitu SVI1I2R (Susceptible, Vaccinated, Infected 1, Infected 2, Recovered) dengan data penduduk Provinsi Daerah Istimewa Yogyakarta dari 3 Maret 2020 hingga 3 November 2021. Tahapan penelitian ini yaitu membentuk model SVI1I2R, menentukan titik ekuilibirum, menentukan bilangan reproduksi dasar, melakukan analisis titik ekuilibrium dan simulasi numerik. Hasil penelitian dari model SVI1I2R yang merupakan persamaan non linier diperoleh titik ekuilibrium bebas penyakit stabil asimtotik pada nilai parameter dan saat. Sedangkan titik ekuilibrium endemik stabil asimtotik pada nilai parameter dan saat sekitar. Artinya setiap individu terinfeksi dapat menginfeksi tiga hingga tujuh individu baru, sehingga kasus positif Covid–19 akan terus bertambah dan menjadi endemik. Dari hasil penelitian dapat disimpulkan bahwa semakin besar laju vaksinasi dapat menekan kasus positif Covid–19.Kata kunci: Covid–19, model SVI1I2R, vaksinasi, analisis kestabilan, titik ekuilibrium.
ANALISIS BIFURKASI PADA MODEL MATEMATIS PREDATOR PREY DENGAN DUA PREDATOR Lia Listyana; Hartono .; Kus Prihantoso Krisnawan
Jurnal Kajian dan Terapan Matematika Vol 5, No 6 (2016): Jurnal Matematika
Publisher : Jurnal Kajian dan Terapan Matematika

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Penelitian ini bertujuan untuk menganalisis model matematis sistem  predator prey  dengan dua predator dan  mengetahui jenis  bifurkasi  sistem  tersebut  dengan  perubahan  laju  kematian  kedua jenis  predator. Model predator  prey  dengan  dua  predator  memiliki  lima  titik  ekuilibrium  yang  keberadaan  tiga  di  antaranya bergantung pada laju kematian kedua jenis  predator  dan titik ekuilibrium yang lain tidak bergantung pada laju kematian kedua jenis  predator. Kestabilan masing-masing titik ekuilibrium ditentukan berdasarkan nilai eigen masing-masing  titik  ekuilibrium.  Perubahan  kestabilan  masing-masing  titik  ekuilibrium  dan  perubahan banyaknya  titik  ekuilibrium  sebagai  penanda  terjadinya  bifurkasi.  Hasil  perhitungan  nilai  eigen  dan  analisis secara  numerik  menunjukkan  terjadinya  bifurkasi  pada  sistem  predator  prey  dengan  dua  predator  saat  laju kematian  predator  jenis I adalah         per satuan waktu dan laju kematian  predator  jenis II adalah        per satuan waktu.Kata kunci : sistem predator prey, sistem predator prey dengan dua predator, titik ekuilibrium, bifurkasi
ANALISIS DINAMIK DARI MODEL MATEMATIKA PADA PENJERNIHAN AIR YANG TERKONTAMINASI LOGAM BERAT DENGAN MENGGUNAKAN BAKTERI BACILLUS SUBTILIS Riris Eka Lestari; Hartono .; Kus Prihantoso Krisnawan
Jurnal Kajian dan Terapan Matematika Vol 5, No 6 (2016): Jurnal Matematika
Publisher : Jurnal Kajian dan Terapan Matematika

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Penelitian  ini  bertujuan  untuk  membentuk  model  matematika  dari  penjernihan  air  yang terkontaminasi logam berat dan menganalisa kestabilan titik ekuilibrium dari sistem tersebut. Penjernihan air  dilakukan  dengan  menggunakan  bakteri  B.subtilis.  Tahapan  dalam  penelitian  ini  yaitu  membentuk model  predator-prey  dengan  fungsi  repon  tak  monoton,  mencari  titik  ekuilibrium,  menentukan  nilai  ????(tingkat kematian bakteri)  dan  ????  (tingkat pertambahan logam)  dan  menganalisis kestabilan di sekitar titik ekuilibrium.  Diperoleh  dua  model  matematika  yaitu  model  pipa  tertutup  dan  model  pipa  terbuka  yang merupakan pengembangan dari model  predator-prey    dengan fungsi respon tak monoton.  Hasil analisis menunjukkan  bahwa  model  pipa  tertutup  dengan  nilai  ???? = 9,  memiliki  tiga  titik  ekuilibrium  dengan semua titik ekuilibrium bernilai tidak stabil untuk semua nilai ????. Model pipa terbuka memiliki jumlah titik ekuilibrium yang berbeda-beda tergantung pada nilai  ????  dan  ????.  Pada model pipa terbuka  titik  ????1= (0,0)????stabil  saat nilai   ???? 0  dan   ???? 0,  ????2stabil  saat nilai  ???? 0  dan  0 ???? 0.202034  dan  ????3stabil  saat nilai ???? 0  dan  −0.202034 ≤ ???? 0.  Dengan  menggunakan  kriteria  Dulac,  diketahui  bahwa  sistem  tidak memiliki periodik orbit.Kata kunci:  Model  predator-prey, fungsi respon tak monoton, model  pipa tertutup,  model pipa terbuka, analisis kestabilan.
Co-Authors Atmini Dhoruri Emut Emut Fitriana Yuli Saptaningtyas Hartono ' Hartono . Hartono Hartono Hartono Hartono Hartono Hartono Himmawati Puji Lestari Husna Arifah Husna Arifah, Husna Lia Listyana Nikenasih Binatari Riris Eka Lestari Wiwit Wahyuningsih