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All Journal MUSTEK ANIM HA Desimal: Jurnal Matematika BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) MATAPPA: Jurnal Pengabdian Kepada Masyarakat JURNAL SILOGISME : Kajian Ilmu Matematika dan Pembelajarannya JPM : Jurnal Pendidikan Matematika Klorofil: Jurnal Penelitian Ilmu-Ilmu Pertanian MATHEMA: JURNAL PENDIDIKAN MATEMATIKA Jurnal Inovasi Pembelajaran Matematika (JIPM)
Pratama, Rian Ade
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Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Mathematics Mechanical Engineering Physics Social Sciences Transportation

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IMPACT OF FEAR BEHAVIOR ON PREY POPULATION GROWTH PREY-PREDATOR INTERACTION Pratama, Rian Ade
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 2 (2022): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (757.075 KB) | DOI: 10.30598/barekengvol16iss2pp371-378

Abstract

Experiments on the living environment of vertebrate ecosystems, it has been shown that predators have a massive influence on the demographic growth rate of prey. The proposed fear effect is a mathematical model that affects the reproductive growth rate of prey with the Holling Type I interaction model. Mathematical analysis of the prey-predator model shows that a strong anti-predator response can provide stability for prey-predator interactions. The parameter area taken will be shown for the extinction of the prey population, the balance of population survival, and the balance between the prey birth rate and the predator death rate. Numerical simulations were given to investigate the biological parameters of the population (birth rate, natural mortality of prey, and predators). Another numerical illustration that is seen is the behavior of prey which is less sensitive in considering the risk of predators with the growth rate of prey.
Dynamical of Prey Refuge in a Diased Predator-Prey Model with Intraspecific Competition for Predator Pratama, Rian Ade
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i2.19893

Abstract

The predator-prey model described is a population growth model of an eco-epidemiological system with prey protection and predator intraspecific traits. Predation interactions in predator species use response functions. The aim of this research is to examine the local stable balance point and look at the characteristics of species resulting from mathematical modeling interventions. Review of balance point analysis, numerical simulation and analysis of given trajectories. The research results show the shape of the model which is arranged with a composition of 5 balance points. There is one rational balance point to be explained, using the Routh-Hurwitz criterion, . The characteristic equation and associated eigenvalues in the mathematical model are the local asymptotically stable balance points. In the trajectory analysis, local stability is also shown by the model formed. There are differences for each population to reach its point of stability. The role of prey protection behavior is very effective in suppressing the spread of disease. Meanwhile, intraspecific predator interactions are able to balance the decreasing growth of prey populations. If we increase the intraspecific interaction coefficient, we can be sure that the growth of the prey population will both increase significantly. When the number of prey populations increases significantly, of course disease transmission and prey protection become determining factors, the continuation of the model in exosite interactions. In prey populations and susceptible prey to infection, growth does not require a long time compared to the growth of predator populations. The time required to achieve stable growth is rapid for the prey species. Although prey species' growth is more fluctuating compared to predator populations. Predatory species are more likely to be stable from the start of their growth. The significance of predatory growth is only at the beginning of growth, while after that it increases slowly and reaches an ideal equilibrium point. Each species has its own characteristics, so extensive studies are needed on more complex forms of response functions in further research. 
The Impact of Peer Pressure Mathematical Models Armed Criminal Groups with Criminal Mapping Area Pratama, Rian Ade; Ruslau, Maria F V
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 4 (2023): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i4.16255

Abstract

Model Armed Criminal Groups is mathematically realistic to be considered in the study of mathematical science. The aim of this research is to form a mathematical model of social cases of criminal acts. The given model is a criminal form that adopts the conformity of the conditions in the susceptible, exposed, infected, and recovered (SEIR) disease distribution model. The research method used is literature study and analysis. The research results show that there are 2 non-negative equilibrium, and one of them is stability analysis. Stability analysis is only carried out at equilibrium that does not contain a zero value with the Routh-Hurwitz criteria. In the results of other research the trajectories show that population growth tends not to experience fluctuations, this indicates that the population is growing towards stability rapidly. In case studies in the field, this marks a cycle of crime that quickly subsides or only occurs in a short period of time and does not occur in a sustainable manner. Overall the susceptible population, the exposed population, the infected population, and the recovered population experience the same conditions.
Analysis Dynamics Two Prey of a Predator-Prey Model with Crowley–Martin Response Function Pratama, Rian Ade; Toaha, Syamsuddin
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.14506

Abstract

The predator-prey model has been extensively developed in recent research. This research is an applied literature study with a proposed dynamics model using the Crowley–Martin response function, namely the development of the Beddington-DeAngelis response function. The aim of this research is to construct a mathematical model of the predator-prey model, equilibrium analysis and population trajectories analysis. The results showed that the predator-prey model produced seven non-negative equilibrium points, but only one equilibrium point was tested for stability. Stability analysis produces negative eigenvalues indicating fulfillment of the Routh-Hurwitz criteria so that the equilibrium point is locally asymtotically stable. Analysis of the stability of the equilibrium point indicates stable population growth over a long period of time. Numerical simulation is also given to see the trajectories of the population growth movement. The population growth of first prey and second prey is not much different, significant growth occurs at the beginning of the growth period, while after reaching the peak the trajectory growth slopes towards a stable point. Different growth is shown by the predator population, which grows linearly with time. The growth of predators is very significant because predators have the freedom to eat resources. Various types of trajectory patterns in ecological parameters show good results for population growth with the given assumptions.
Dynamics of predator–prey populations with allee effects under the influence of two generalist predators Pratama, Rian Ade; Suryani, Dessy Rizki; Ruslau, Maria F V
Desimal: Jurnal Matematika Vol. 8 No. 3 (2025): Desimal: Jurnal Matematika
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/djm.v8i3.202528849

Abstract

In this study, we analyze a predator–prey model incorporating a Holling type II functional response, an Allee effect in the prey population, and generalist predator species. The proposed interaction model is formulated as a nonlinear differential system involving three species: one prey species and two generalist predator species. The research methodology combines literature review and analytical investigation. The objectives are to examine the equilibrium points, assess stability using the Routh–Hurwitz criteria, and perform numerical simulations to illustrate population growth trajectories. The analysis reveals eleven equilibrium points, consisting of trivial, semi-trivial, and coexistence equilibria. Among the coexistence equilibria, only one satisfies the local stability conditions, as determined by the characteristic equation associated with the Routh–Hurwitz criteria. The characteristic equation of the model is a complex quartic polynomial. Ecologically, such local stability conditions ensure the persistence of all species within the ecosystem. Numerical simulations are also provided for the proposed model, demonstrating stable conditions for all three populations. However, the population growth patterns of the three species differ significantly. The prey population exhibits pronounced fluctuations: initially showing a gradual change, followed by a rapid increase once predation occurs, eventually reaching a stable state. Interestingly, during predation events, the overall prey population size experiences substantial growth. When predation proceeds without significant hindrance, predator populations also increase simultaneously. The interplay between the Allee effect and the Holling type II functional response plays a critical role in determining the numerical dynamics of the predator–prey system.
ANALYSIS DINAMIC AND BIOECONOMIC OF A PREDATOR-PREY SYSTEM WITH MARINE NATIONAL PARK Pratama, Rian Ade; Wahyudi, Candra Agus
Jurnal Silogisme : Kajian Ilmu Matematika dan Pembelajarannya Vol 8 No 1 (2023): Juni
Publisher : Universitas Muhammadiyah Ponorogo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24269/silogisme.v8i1.6771

Abstract

In the study of fisheries or marine products in developing countries, the problem of managing marine resources is often faced. Excessive exploitation due to weak legal and supervisory sectors is the most frequently used factor. This research involves a predator-prey mathematical model and provides an intervention variable exploitation, namely harvest. Harvest is carried out on two types of species that inhabit two protected areas of the marine national park zone. One of the objectives of the exploitation variable is to provide benefits for harvesters, such as fishermen. Boundary areas in the marine national park zone and points of equilibrium are assigned to research wetting. Stability analysis using the Routh-Hurwitz criteria indicates the survival of the population. The predator-prey model formed resulted in seven non-negative equilibria, but only one equilibrium point met the research assumptions. Numerical simulations are also provided in trajectories from the initial model formation to the bionomic shape. The basic assumption is that harvesting is carried out in the marine national park zone harvesting is carried out only in a limited way. In the prey one population, more can be harvested in the region than the prey two population. Ecologically, the population of prey one lives in a larger carrying capacity area. In the predator-prey model system, the predator-prey model makes it possible to harvest populations that live in a wider area. The wider the area of the marine national park zone, the more it is permitted to carry out exploitation efforts, provided that it is still limited.
Application of Beddington DeAngelis Response Function in Ecological Mathematical System: Study Fish Endemic Oliv Predator Species in Merauke Pratama, Rian Ade; Ruslau, Maria Fransina Veronica
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 1 (2022): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i1.5340

Abstract

Predator-prey type fishery models Oliv fish is a trans-endemic predator species that inhabits freshwater swamps and brackish water in Merauke, Papua. Maintaining the survival of the Oliv fish species is the main reason for compiling a mathematical model, so that it can be considered by local governments in making ecological policies. Method on model discussed is assembled with the growth of predator-prey populations following the growth of logistics. The response or predatory function corresponding to the behavior of endemic Oliv fish is the Beddington DeAngelis type. The growth of predatory species uses the concept of growth with stage structure, are divided into mature and immature. Research results show there are four equilibrium points of the mathematical model, but only one point becomes the asymptotic stable equilibrium point without harvesting W_4 (x^*,y^*,z^* )=92.823,1311.489,525.957 and equilibrium point with harvesting W_4 (x^*,y^*,z^* )=95.062,92.639,160.466 . Harvesting exploitation efforts are carried out by the community so that the harvesting variables are added with a proportional concept. Simulation of the results of the study shows a stable scheme and harvesting conducted can maintain the number of populations that continue. 
Trajectories of Cannibalism Interaction with Holling Type II and Monod–Haldane Functional Responses Pratama, Rian Ade; Suryani, Dessy Rizki; Ruslau, Maria F. V.; Meirista, Etriana
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 10, No 2 (2026): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v10i2.36659

Abstract

The stability and equilibrium behavior of predator–prey systems involving cannibalistic interactions is crucial for explaining the long-term sustainability of ecological communities. This study aims to analyze the dynamics of a modified predator–prey model by incorporating cannibalism in predators as a self-regulating mechanism influencing population control. This study is a literature-based research, and the instruments employed are non-physical in nature, including a mathematical model, mathematical analysis tools, and numerical computation frameworks. The research methodology employs literature review and analysis of a model formulated as a system of nonlinear differential equations.  This system describes the population dynamics of two prey species and one predator species exhibiting cannibalistic tendencies. Analytical and numerical approaches are utilized to determine equilibrium points, evaluate local stability, and assess the effects of density-dependent mortality and cannibalistic behavior on ecosystem balance. The results show that the proposed predator–prey model admits one trivial equilibrium, five semi-trivial equilibrium, and one coexistence equilibrium. The coexistence equilibrium is locally asymptotically stable and satisfies the Routh–Hurwitz stability criterion. Simulation numeric the cannibalism parameter and density-dependent mortality rates play a significant role in stabilizing the predator population dynamics. When the mortality coefficient increases, the predator population decreases toward a lower equilibrium point, while the prey population slightly increases due to reduced predation pressure. Eigenvalue analysis reinforces these findings by confirming the system's compliance with the Routh–Hurwitz stability conditions. Ecological implications, these findings suggest that cannibalistic behavior in predators acts as a natural feedback mechanism to regulate population density, enhance ecosystem stability, and support the long-term sustainability of predator–prey interactions. The cannibalistic character of the predator species does not necessarily lead to species extinction, but can instead facilitate a sustainable and balanced coexistence within the ecosystem.
Co-Authors Amil Siddik, A. Muh. Aminah, R. Iin Siti Dadi, Oswaldus Henie Poerwandar Asmaningrum, Henie Poerwandar Ika Paridawati Iriani, Cindy Dian Kasbawati Kasbawati Maria Fransina Veronica Ruslau Meirista, Etriana Natsir, Irmawaty Nur?aini, Khumaeroh Dwi Nurbaiti Amir Nurhayati Nurhayati Nurhayati Palobo, Markus Ruslau, Maria F V Ruslau, Maria F V. Ruslau, Maria F. V. Ruslau, Maria Fransina Veronica Suryani, Dessy Rizki syamsuddin Toaha Taufik, Abdul Rachman Wahyudi, Candra Agus