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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Jambura Journal of Biomathematics (JJBM)
Isnani Darti
University of Brawijaya
Computer Science & IT Decision Sciences, Operations Research & Management Mathematics

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A dynamical analysis of a predator-prey model: Exploring the influence of the Allee effect, environmental protection, and supplementary food sources Resmawan Resmawan; Agus Suryanto; Isnani Darti; Hasan S. Panigoro
Jambura Journal of Biomathematics (JJBM) Volume 6, Issue 4: December 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v6i4.32685

Abstract

This paper introduces a new predator-prey model with supplementary food sorces for the predator and the Allee effect on prey. Analytical proof of the existence, uniqueness, non-negativity, and boundedness of the solutions validates the model. Three equilibrium points are found: a trivial point, whose local stability depends on the Allee effect’s strength; a semi-trivial point, and an interior point whose local stability depends on certain conditions. The Lyapunov function and La Salle invariance principle show that each equilibrium point is globally asymptotically stable. The system displays intricate dynamical behaviors, including forward and Hopf bifurcations, along with bistability, which is regulated by critical parameters such as the predation conversion rate, environmental protection rate, and supplementary food sources. Under a weak Allee effect, increasing the predation conversion rate or supplementary food can shift the system from predator extinction to oscillatory coexistence. In contrast, under a strong Allee effect, these increases may instead drive both species to extinction if thresholds are exceeded. Moreover, variations in environmental protection rate yield contrasting outcomes: while a higher rate under weak Allee conditions may stabilize prey and eliminate predators, under strong Allee conditions, it may lead to total extinction. These findings illustrate the intricate relationship between biological and environmental components, highlighting the necessity for preventive measures and supplementary resources in population outcomes. The findings indicate that environmental protection and supplementary food sources influence species persistence and extinction in predator-prey dynamics, which is crucial for ecological conservation.
Logistic Map with Feedback Control for Resilient Image Encryption Mohammad Fahrurrozy; Agus Suryanto; Isnani Darti
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of 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 Hasan S. Panigoro Mohammad Fahrurrozy Resmawan Resmawan