Conditions for Ultimate Boundedness of Solutions and Permanence for a Hybrid Lotka–Volterra System

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Conditions for Ultimate Boundedness of Solutions and Permanence for a Hybrid Lotka–Volterra System. / Платонов, Алексей Викторович.

In: Russian Mathematics, Vol. 68, No. 6, 01.06.2024, p. 58-67.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{bf41f653d8a647128c65f9212810a657,

title = "Conditions for Ultimate Boundedness of Solutions and Permanence for a Hybrid Lotka–Volterra System",

abstract = "Abstract: In the paper, a generalized Lotka–Volterra-type system with switching is considered. The conditions for the ultimate boundedness of solutions and the permanence of the system are studied. With the aid of the direct Lyapunov method, the requirements for the switching law are established to guarantee the necessary dynamics of the system. An attractive compact invariant set is constructed in the phase space of the system, and a given region of attraction for this set is provided. A distinctive feature of the work is the use of a combination of two different Lyapunov functions, each of which plays its own special role in solving the problem.",

keywords = "generalized Lotka–Volterra system, permanence, switching, ultimate boundedness of solutions",

author = "Платонов, {Алексей Викторович}",

year = "2024",

month = jun,

day = "1",

doi = "10.3103/s1066369x24700440",

language = "English",

volume = "68",

pages = "58--67",

journal = "Russian Mathematics",

issn = "1066-369X",

publisher = "Allerton Press, Inc.",

number = "6",

}

RIS

TY - JOUR

T1 - Conditions for Ultimate Boundedness of Solutions and Permanence for a Hybrid Lotka–Volterra System

AU - Платонов, Алексей Викторович

PY - 2024/6/1

Y1 - 2024/6/1

N2 - Abstract: In the paper, a generalized Lotka–Volterra-type system with switching is considered. The conditions for the ultimate boundedness of solutions and the permanence of the system are studied. With the aid of the direct Lyapunov method, the requirements for the switching law are established to guarantee the necessary dynamics of the system. An attractive compact invariant set is constructed in the phase space of the system, and a given region of attraction for this set is provided. A distinctive feature of the work is the use of a combination of two different Lyapunov functions, each of which plays its own special role in solving the problem.

AB - Abstract: In the paper, a generalized Lotka–Volterra-type system with switching is considered. The conditions for the ultimate boundedness of solutions and the permanence of the system are studied. With the aid of the direct Lyapunov method, the requirements for the switching law are established to guarantee the necessary dynamics of the system. An attractive compact invariant set is constructed in the phase space of the system, and a given region of attraction for this set is provided. A distinctive feature of the work is the use of a combination of two different Lyapunov functions, each of which plays its own special role in solving the problem.

KW - generalized Lotka–Volterra system

KW - permanence

KW - switching

KW - ultimate boundedness of solutions

UR - https://www.mendeley.com/catalogue/c9cde74e-7c28-33dc-ab54-461c54f22ee3/

U2 - 10.3103/s1066369x24700440

DO - 10.3103/s1066369x24700440

M3 - Article

VL - 68

SP - 58

EP - 67

JO - Russian Mathematics

JF - Russian Mathematics

SN - 1066-369X

IS - 6

ER -

ID: 124202964