Lotka-Volterra Model with Two Predators and Their Prey

Hadžiabdić, Vahidin; Mehuljić, Midhat; Bektešević, Jasmin

doi:10.18421/tem61-19

Cited by 3 publications

(4 citation statements)

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“…The condition (2) of theorem 1 directly yields from (21). The passive output (22) was computed based on equation (3).…”

Section: Passivity Of Lotka-volterra Systemsmentioning

confidence: 99%

“…Consider an open Lotka-Volterra system in which the state dynamics is defined by ( 17) and the output is given by (22).…”

Section: Feedback Equivalence Of Lotka-volterra Systems To Passive Sy...mentioning

confidence: 99%

“…The system with u c = w = 0 admits non-zero equilibrium points for all the three populations only if m 21 /l 2 = m 31 /l 3 , which is an eminently restrictive condition. Otherwise, one of the predator species dies out [22] and the dynamics of the system degenerates to a twodimensional Lotka-Volterra system, see example 1. However, using feedback control, the non-zero equilibrium for all the three species' populations can be assured.…”

Section: Lotka-volterra Modelmentioning

confidence: 99%

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Passivity of Lotka–Volterra and quasi-polynomial systems

2021

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This study approaches the stability analysis and controller design of Lotka–Volterra and quasi-polynomial systems from the perspective of passivity theory. The passivity based approach requires to extend the autonomous system model with a suitable input structure. The condition of passivity for Lotka–Volterra systems is less strict than the classic asymptotic stability criterion. It is shown that each Lotka–Volterra system is feedback equivalent to a passive system and a passifying state feedback controller is proposed. The passivity based approach enables the design of novel state feedback controllers to Lotka–Volterra systems. The asymptotic stability can be achieved by applying an additional diagonal state feedback having arbitrarily small gains. This result was further explored to achieve rate disturbance attenuation in controlled Lotka–Volterra systems. By exploiting the dynamical similarities between the Lotka–Volterra and quasi-polynomial systems, it was shown that the passivity related results, developed for Lotka–Volterra systems, are also valid for a large class of quasi-polynomial systems. The methods and tools developed have been illustrated through simulation case studies.

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“…The condition (2) of theorem 1 directly yields from (21). The passive output (22) was computed based on equation (3).…”

Section: Passivity Of Lotka-volterra Systemsmentioning

confidence: 99%

“…Consider an open Lotka-Volterra system in which the state dynamics is defined by ( 17) and the output is given by (22).…”

Section: Feedback Equivalence Of Lotka-volterra Systems To Passive Sy...mentioning

confidence: 99%

Section: Lotka-volterra Modelmentioning

confidence: 99%

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Passivity of Lotka–Volterra and quasi-polynomial systems

2021

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“…Dalam Ekologi yang sangat komplek, perlu diketahui beberapa perilaku makhluk hidup yang saling menguntungkan bagi makhluk hidup yang lain atau bahkan merugikan [3], untuk itu pembahasan mengenai perilaku dinamik beberapa Model predator prey yang lain adalah model lotka voltera, dengan melihat dua spesies Prey sebagai mangsa dan predator sebagai pemangsa. Model pemangsa-pemangsa Lotka-Volterra dua dimensi yang dimodifikasi juga menggunakan sistem persamaan nonlinier yang mencakup pertumbuhan logistik dua spesies, carrying capacity mangsa, daya dukung predator dan faktor predator telah dibahas oleh [4] dan [5].…”

Section: Pendahuluanunclassified

Pengaruh Eksploitasi Berlebihan Populasi Prey Pada Model Predator Prey Holling Ii, Pemanenan Dan Perlindungan Prey

Pusawidjayanti¹

2021

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Pada artikel ini, kami membahas tentang model predator prey dengan fungsi respon holling tipe II, perlindungan pada prey dan pemanenan pada kedua populasi. Hal ini diasumsikan bahwa laju pertumbuhan prey lebih tinggi dibandingkan dengan laju pemanenan. Model ini ditemukan ada tiga titik equilibrium yaitu dan . Simulasi numerik ditunjukkan tidak hanya untuk memperlihatkan titik equilibriumnya tetapi juga untuk melihat efek eksploitasi pada populasi prey. Hasil dari penelitian ini adalah jika populasi prey di ekploitasi secara besar-besaran akan menyebabkan kepunahan pada populasi prey.Kata Kunci: eksploitasi, populasi, pemanenan dan perlindungan.

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Dynamical Analysis Predator-Prey Population with Holling Type II Functional Response

Pusawidjayanti

Asmianto

Kusumasari

2021

J. Phys.: Conf. Ser.

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In this article, we investigate the dynamical analysis of predator prey model. Interaction among preys and predators use Holling type II functional response, and assuming prey refuge as well as harvesting in both populations. This study aims to study the predator prey model and to determine the effect of overharvesting which consequently will affect the ecosystem. In the model found three equilibrium points, i.e., E 1(0,0) is the extinction of predator and prey equilibrium, E 2(x 2, 0) is the equilibrium with predatory populations extinct and the last equilibrium points E 3 (x 3, y 3) is the coexist equilibrium. All equilibrium points are asymptotically stable (locally) under certain conditions. These analytical findings were confirmed by several numerical simulations.

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Lotka-Volterra Model with Two Predators and Their Prey

Cited by 3 publications

References 4 publications

Passivity of Lotka–Volterra and quasi-polynomial systems

Passivity of Lotka–Volterra and quasi-polynomial systems

Pengaruh Eksploitasi Berlebihan Populasi Prey Pada Model Predator Prey Holling Ii, Pemanenan Dan Perlindungan Prey

Dynamical Analysis Predator-Prey Population with Holling Type II Functional Response

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