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All Journal InPrime: Indonesian Journal Of Pure And Applied Mathematics Research in the Mathematical and Natural Sciences
Al Idrus, Ainun Sukmawati
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Computer Science & IT Education Mathematics

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Analisis Dinamik Model Predator-Prey dengan Struktur Usia dan Perilaku Anti-Predator Al Idrus, Ainun Sukmawati; Abd. Gani, Ayub Prianto; Zaid, Nurlaila
Research in the Mathematical and Natural Sciences Vol. 1 No. 2 (2022): May-October 2022
Publisher : Scimadly Publishing

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (303.085 KB) | DOI: 10.55657/rmns.v1i2.63

Abstract

This article discusses the Predator-prey Holling type II model involving age structure and anti-predator behaviour. The age structure is given to the predator population, which is divided into two, namely juvenile predators and adult predators, while in the prey population, there is anti-predator behaviour, namely the tendency to defend against predator attacks. The model analysis includes the determination of a fixed point, analysis of the stability of the fixed point and numerical simulation. Three fixed points were obtained, namely the fixed point of population extinction (), the fixed point of predator extinction and the fixed point of population existence. Stability analysis shows that is always a saddle while and are conditionally stable. Furthermore, it is shown that the two conditions are both stable nodes. At the end, a simulation shows that the population dynamics that occur are highly dependent on the initial conditions of the population and the value of the anti-predator behaviour parameter of the prey population.
Existence and Uniqueness of Fixed Point for Cyclic Mappings in Quasi-αb-Metric Spaces Al Idrus, Ainun Sukmawati; Resmawan, Resmawan; Payu, Muhammad Rezky Friesta; Nasib, Salmun K.; Asriadi, Asriadi
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 4, No 1 (2022)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v4i1.24462

Abstract

The fixed point theory remains the most important and preferred topic studied in mathematical analysis. This study discusses sufficient conditions to prove a unique fixed point in quasi-αb-metric spaces with cyclic mapping. The analysis starts by showing fulfillment of the cyclic Banach contraction and proving the Cauchy sequence as a condition for proving a unique fixed point in quasi-αb-metric spaces with cyclic mapping. Furthermore, it's shown that the cyclic mappings, T have a unique fixed point in quasi-αb-metric spaces. Finally, an example is given to strengthen the proof of the theorems that have been done.Keywords: fixed point theory; Quasi -Metric spaces; Cyclic Banach Contraction; Cauchy sequence. AbstrakTeori titik tetap termasuk salah satu topik penting dan menarik untuk diteliti pada bidang analisis. Pada penelitian ini, dibahas tentang syarat cukup dalam membuktikan bahwa terdapat titik tetap tunggal dalam ruang quasi- b-metrik pada pemetaan siklik. Analisis diawali dengan menunjukkan pemenuhan kondisi kontraksi Banach siklik dan pembuktian barisan Cauchy sebagai syarat pembuktian bahwa terdapat titik tetap tunggal pada pemetaan siklik dalam ruang quasi- b-metrik. Selanjutnya ditunjukkan bahwa pemetaan siklik  memiliki titik tetap tunggal dalam ruang quasi b-metrik. Terakhir, diberikan contoh untuk memperkuat pembuktian teorema yang telah dilakukan.Kata Kunci: teori titik tetap; ruang Quasi -Metrik; Kontraksi Banach Siklik; barisan Cauchy.
Co-Authors Abd. Gani, Ayub Prianto Resmawan Resmawan Salmun K. Nasib Sembiring, Rinawati Zaid, Nurlaila