Integrable Lotka-Volterra systems

被引：26
|
作者：
Bogoyavlenskij, O. I. [1 ,2 ]
机构：
[1] Queens Univ, Dept Math, Kingston, ON K7L 3N6, Canada
[2] Russian Acad Sci, VA Steklov Math Inst, Moscow 119991, Russia
来源：
REGULAR & CHAOTIC DYNAMICS | 2008年 / 13卷 / 06期
关键词：
Lax representation; Hamiltonian structures; Casimir functions; Riemannian surfaces; Lotka-Volterra systems; integrable lattices;
D O I：
10.1134/S1560354708060051
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Infinite- and finite-dimensional lattices of Lotka-Volterra type are derived that possess Lax representations and have large families of first integrals. The obtained systems are Hamiltonian and contain perturbations of Volterra lattice. Examples of Liouville-integrable 4-dimensional Hamiltonian Lotka-Volterra systems are presented. Several 5-dimensional Lotka- Volterra systems are found that have Lax representations and are Liouville-integrable on constant levels of Casimir functions.
引用
收藏
页码：543 / 556
页数：14
相关论文
共 50 条
  • [1] Integrable Lotka-Volterra systems
    O. I. Bogoyavlenskij
    Regular and Chaotic Dynamics, 2008, 13 : 543 - 556
  • [2] Integrable deformations of Lotka-Volterra systems
    Ballesteros, Angel
    Blasco, Alfonso
    Musso, Fabio
    PHYSICS LETTERS A, 2011, 375 (38) : 3370 - 3374
  • [3] Lotka-Volterra systems integrable in quadratures
    Bogoyavlenskij, Oleg
    Itoh, Yoshiaki
    Yukawa, Tetsuyuki
    JOURNAL OF MATHEMATICAL PHYSICS, 2008, 49 (05)
  • [4] Integrable and non-integrable Lotka-Volterra systems
    Bountis, Tassos
    Zhunussova, Zhanat
    Dosmagulova, Karlygash
    Kanellopoulos, George
    PHYSICS LETTERS A, 2021, 402
  • [5] A NEW CLASS OF INTEGRABLE LOTKA-VOLTERRA SYSTEMS
    Christodoulidi, Helen
    Hone, Andrew N. W.
    Kouloukas, Theodoros E.
    JOURNAL OF COMPUTATIONAL DYNAMICS, 2019, 6 (02): : 223 - 237
  • [6] INTEGRABLE DISCRETISATION OF THE LOTKA-VOLTERRA SYSTEM
    He, Yang
    Sun, Yajuan
    Shang, Zaijiu
    JOURNAL OF COMPUTATIONAL MATHEMATICS, 2015, 33 (05): : 468 - 494
  • [7] On an Integrable Discretisation of the Lotka-Volterra System
    He, Yang
    Sun, Yajuan
    NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2012), VOLS A AND B, 2012, 1479 : 1295 - 1298
  • [8] Integrable reductions of the Bogoyavlenskij-Itoh Lotka-Volterra systems
    Damianou, P. A.
    Evripidou, C. A.
    Kassotakis, P.
    Vanhaecke, P.
    JOURNAL OF MATHEMATICAL PHYSICS, 2017, 58 (03)
  • [9] Integrable deformations of the Bogoyavlenskij-Itoh Lotka-Volterra systems
    Evripidou, C. A.
    Kassotakis, P.
    Vanhaecke, P.
    REGULAR & CHAOTIC DYNAMICS, 2017, 22 (06): : 721 - 739
  • [10] Whence Lotka-Volterra?: Conservation laws and integrable systems in ecology
    O'Dwyer, James P.
    THEORETICAL ECOLOGY, 2018, 11 (04) : 441 - 452
12345