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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Limits: Journal of Mathematics and Its Applications
Fahrurrozy, Mohammad
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Computer Science & IT Mathematics

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Bifurkasi pada Model Predator-Prey Diskret dengan Fungsi Respon Ratio-Depedent dan Pemanenan Suryanto, Agus; Krisnawati, Vira Hari; Lestari, Sri Puji; Matatula, Denis Andre; Fahrurrozy, Mohammad
Limits: Journal of Mathematics and Its Applications Vol. 22 No. 2 (2025): Limits: Journal of Mathematics and Its Applications Volume 22 Nomor 2 Edisi Ju
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v22i2.3450

Abstract

This article discusses a predator-prey model with a ratio-dependent functional response and harvesting in both populations.  The differential equation of predator-prey model is discretized using the Euler method. The dynamics of the obtained discrete time model are investigated by determining the fixed points as well as their stability properties, and bifurcation analysis. Bifurcation analysis shows that the discrete time model can experience bifurcation, both period-doubling bifurcation and Neimark-Sacker bifurcation, when the value of time-integration step  passes a critical value. The analysis results have been confirmed by our numerical simulation results presented at the end of this article.
Logistic Map with Feedback Control for Resilient Image Encryption Fahrurrozy, Mohammad; Suryanto, Agus; Darti, Isnani
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i1.30783

Abstract

Images are one of many forms used to store important information that is easy to use and share, but they are vulnerable to cyber-attacks. An encryption effort is needed to secure the vital information in an image. In this paper, an encryption and decryption algorithm for grayscale and RGB images is proposed using logistic map with feedback control (LMFC). This 2D map which is an improvement from the popular one-dimensional logistic map also exhibits sensitive dependence on initial conditions, known as chaos. This phenomenon is verified through bifurcation diagram and the largest Lyapunov exponent. By using the largest Lyapunov exponent and the control parameters as secret key, LMFC generates two sequences of pseudo-random number related to the original image. Subsequently, a permutation process is proposed, utilizing permutation box to rearrange the pixel positions in the plain image. Finally, a diffusion process is proposed, utilizing XOR operations and keystreams created from the pseudo-random sequence to alter the pixel values, resulting in a visually distinct cipher image. Performance analysis of the proposed algorithm indicates resilience to various cryptanalysis and robust security, as it is sensitive to both secret keys and plain image. Additionally, the proposed decryption algorithm demonstrates the ability to reconstruct the original image with good quality from a cipher image, despite data changes or losses.
Co-Authors Agus Suryanto Isnani Darti Krisnawati, Vira Hari Matatula, Denis Andre Sri Puji Lestari