TARU PUBLICATIONS
Journal of Dynamical Systems and Geometric Theories cover

Journal of Dynamical Systems and Geometric Theories

(Since 2002)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0057·ISSN (Print): 1726-037X
Powered by:Powered by

The Journal of Dynamical Systems and Geometric Theories (JDSGT) is a world leading journal publishing high quality, rigorously peer-reviewed original research on dynamical systems and geometry, including the interactions between these two subjects and interdisciplinary research with other branches of knowledge since 2003. Topics published by the Journal include but are not limited to: Random dynamical systems Geometry and physics Dynamical systems with hyperbolic behaviour Real and complex geometry Ergodic theory Distance geometry Topological dynamics Global differential geometry Infinite-dimensional Hamiltonian systems Symplectic geometry, contact geometry The journal considers original research articles, survey articles, and book reviews for publication. Responses to articles and correspondence will also be considered at the Chief Editor’s discretion.

Issues up to 2022 co-published with and available at:Taylor & Francis
info@tarupublications.com
Taru Online First Current IssueBrowse all Issues
Journal of Dynamical Systems and Geometric Theories
Open Access Original Articles

Global Stability for the N-Species Lotka-Volterra Tree Systems of Interacting Population-Diffusion Equations

,

* Corresponding author · click or hover a name for details

pp. 7–15Vol. 2Issue 1January 2004DOI: 10.1080/1726037X.2004.10698474XML
Received:
17 Sep 2003
Published Online:
01 Jan 2004
Article type:
Original Articles
Language:
EN
Article no.:
1726037X.2004.10698474
Pages:
7–15

Abstract

Applying invariant region method and with the aid of quadratic form theory we obtain a set of sufficient conditions for the globally asymptotic stability of the solutions to Cauchy problem for the n-species Lotka-Volterra tree systems of interacting population-diffusion equations. The criteria in this paper are in explicit forms of the parameters, and thus, are easily verifiable. Moreover, this criteria is applicable to competition model, cooperation model, as well as to predator-prey model.

Keywords

Cauchy problem for parabolic systemsGlobal stability

References

Chueh, K.N., Conley, C.C. and Smoller, J.1977 . Positive invariant region for systems of nonlinear diffusion equations . Indiana Univ. Math. J, 26 : 373 – 392 . Debnath, L.1997 . Nonlinear Partial Differential Equations for Scientists and Engineers, Boston, Basel, Berlin: Birkhäuser . Gürleback, K. and Sprößig, W.1990 . Quaternionic Analysis and Elliptic Boundary Value Problems, Basel: Birkhäuser . Gürleback, K. and Sprößig, W.1998 . Quaternionic Calculus for Physicists and Engineers, Vol. 1 , New York, Brisbane, Weinhein, Singapore, Toronto: John Wiley & Sons, Chichester . Series Mathematical Problems in Practice Xinhua, Ji. 1991 . “ Global stability for n-dimensional Lotka-Volterra competition simple chain systems ” . In Advances in Dynamical Systems, Edited by: Shiraiwa, K.Vol. 9 , 211 – 222 . World Scientfic Publ . Editor Xinhua, Ji. 1996 . The existence of globally Stable equilibria of n-dimensional Lotka-Volterra systems . Appl. Anal, 62 : 11 – 28 . Li, Xue-Zhi, Tang, Chun-Lei and Ji, Xin-Hua. 2000 . Global asymptotic stability for Lotka-Volterra tree systems . Differential Equations and Dynamical Systems, 8 ( 2 ) : 141 – 149 . Lu, Zhengyi. 1994 . Global stability for the Cauchy problem of a class of reaction-diffusion systems . J.Partial Diff. Eqs, 7 ( 4 ) : 323 – 329 . Smoller, J.1983 . Shock Waves and Reaction-Diffusion Equations, Berlin: Springer-Verlag . Takeuchi, Y., Adachi, N. and Tokumaru, H.1978 . The stability of generalized Volterra equation . J. Math. Anal. Appl, 62 : 453 – 473 . Takeuchi, Y. and Adachi, N.1980 . The existence of globally stable equilibria of ecosystems of the generalized Volterra type . J. Math. Biology, 10 : 401 – 415 . Weighberger, H.1975 . Invariant sets for weakly coupled parabolic and elliptic systems . Rend. Mat, vi ( 8 ) : 295 – 310 .
Views: 5Downloads: 2Citations: 0