Dynamical Analysis of a Predator-Prey Model Incorporating Predator Cannibalism and Refuge

Rayungsari, Maya; Suryanto, Agus; Kusumawinahyu, Wuryansari Muharini; Darti, Isnani

doi:10.3390/axioms11030116

Cited by 16 publications

(15 citation statements)

References 21 publications

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“…Beberapa hasil penelitian yang memfokuskan pada bentuk kanibalisme spesies predator terjadi secara alamiah. Interaksi kanibalisme juga sering terjadi pada kondisi kepadatan populasi yang tinggi dan ketersediaan makanan yang terbatas, atau pada waktu masa transisi proses pencarian makanan yang baru [21]. Secara matematis bentuk fungsi kanibalisme yang diadopsi…”

Section: Metode Penelitian 21 Landasan Teoriunclassified

Model Modifikasi Holling-Tanner dengan Interaksi Kanibalisme dan Sumber Makanan Alternatif pada Predator

Pratama

Suryani²,

Ruslau³

2022

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Penelitian ini mengkaji model pertumbuhan populasi model predator-prey Holling-Tonner yang dimodifikasi. Pertumbuhan model predator-prey yang dianalisis mengadopsi pertumbuhan logistik. Sementara pada fungsi pemangsaan mengikuti model Holling Type II. Variabel yang tidak kalah penting dalam penelitian ini adalah adanya sumber alternatif bagi predator. Konsep seperti ini sangat realistis untuk dipertimbangkan, mengingat banyak spesies predator yang berganti sumber makanan, dikarenakan sumber makanan yang terbatas. Analisis kestabilan dilakukan pada model untuk melihat keberlangsungan populasi dalam jangka waktu yang lama dengan tingkat interaksi yang sesuai. Dari empat titik equilibrium non-negatif yang dihasilkan pada model, pengujian kestabilan hanya dilakukan pada satu titik equilibrium. Secara matematis dilakukan uji Routh-Hurwitz, dengan matriks Jacobian yang bersesuaian. Simulasi numerik menjadi asumsi realistis awal bagi keberlangsungan hidup masing-masing spesies dan melihat karakter dari masingmasing spesies tersebut. Titik equilibrium yang dipilih menjadi pegujian pada kesetabilan asimtotik lokal dan kurva pertumbuhan. Kemungkinan adanya perpindahan sumber makanan sangat mungkin terjadi, sementara interaksi kanibalisme pada model yang dikembangkan tidak memberikan pengaruh yang signifikan pada masing-masing spesies.Kata Kunci: Kanibalisme, makanan alternatif dan Predator-Prey.

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Section: Metode Penelitian 21 Landasan Teoriunclassified

Model Modifikasi Holling-Tanner dengan Interaksi Kanibalisme dan Sumber Makanan Alternatif pada Predator

Pratama

Suryani²,

Ruslau³

2022

JSMS

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“…Some researchers have investigated the mathematical model involving cannibalism [18][19][20][21]. Kang et al [18] studied a single-species cannibalism model with stage structure.…”

Section: Introductionmentioning

confidence: 99%

“…This is known as refuge behavior in the context of ecology. The mathematical model of Predator-prey interaction with prey refuge has also piqued the interest of researchers [21][22][23][24][25]. Rayungsari et al [21] modified model proposed by Deng et al [20] by adding the assumption that there is a refuge in the cannibalized predator population, as much as mP.…”

Section: Introductionmentioning

confidence: 99%

“…The mathematical model of Predator-prey interaction with prey refuge has also piqued the interest of researchers [21][22][23][24][25]. Rayungsari et al [21] modified model proposed by Deng et al [20] by adding the assumption that there is a refuge in the cannibalized predator population, as much as mP. Moreover, it is also assumed that predators need time to catch and handle the prey, so that the rate of prey predation follows the Holling type-II functional response.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics analysis of a predator–prey fractional-order model incorporating predator cannibalism and refuge

Rayungsari

Suryanto

Kusumawinahyu

et al. 2023

Front. Appl. Math. Stat.

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In this article, we consider a predator–prey interaction incorporating cannibalism, refuge, and memory effect. To involve the memory effect, we apply Caputo fractional-order derivative operator. We verify the non-negativity, existence, uniqueness, and boundedness of the model solution. We then analyze the local and global stability of the equilibrium points. We also investigate the existence of Hopf bifurcation. The model has four equilibrium points, i.e., the origin point, prey extinction point, predator extinction point, and coexistence point. The origin point is always unstable, while the other equilibrium points are conditionally locally asymptotically stable. The stability of the coexistence point depends on the order of the Caputo derivative, α. The prey extinction point, predator extinction point, and coexistence point are conditionally globally and asymptotically stable. There exists Hopf bifurcation of coexistence point with parameter α. The analytic results of stability properties and Hopf bifurcations are confirmed by numerical simulations.

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“…Cannibalism and predatory resistance behavior greatly influence the dynamics of the predator-prey model in the ecological world. Theoretically, cannibalism and prey resistance have the ability to reduce the number of populations or inhibit the growth of predators [18]. In the theory of population growth, the nature of cannibalism is very detrimental, because the population is decreasing.…”

Section: Introductionmentioning

confidence: 99%

Dynamics Twin Cannibalism of Two Predator and Two Prey System with Prey Defense

et al. 2022

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The study discusses the condition of the existence of all non-negative equilibrium points. There are 9 realistic equilibrium points from the constructed model. A local stable condition is obtained, a point of equilibrium that is completely biologically feasible. The analytical method on the mathematically formed model is limited, so numerical simulation is also given to explore the model. Numerical simulation is intervened in a model that will show growth in trajectories. The tendency of trajectories in prey one and predator one species is relatively the same because the interactions that occur are intensive. Likewise, prey two and predator two occur, and the interactions that occur cause population growth grow to fluctuate. Differences occur in both types of species, namely predator-prey one and predator-prey two. In the one interaction group, growth tends to be more volatile and moves slowly towards the point of stability in population growth. Incidence is inversely proportional to the interaction of species two which tend to be faster towards the stability point. In general, the results of numerical simulations show that there is a pattern formation in the predator-prey system that grows sustainabley.

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Dynamical Analysis of a Predator-Prey Model Incorporating Predator Cannibalism and Refuge

Cited by 16 publications

References 21 publications

Model Modifikasi Holling-Tanner dengan Interaksi Kanibalisme dan Sumber Makanan Alternatif pada Predator

Model Modifikasi Holling-Tanner dengan Interaksi Kanibalisme dan Sumber Makanan Alternatif pada Predator

Dynamics analysis of a predator–prey fractional-order model incorporating predator cannibalism and refuge

Dynamics Twin Cannibalism of Two Predator and Two Prey System with Prey Defense

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