On global dynamics of type-k competitive Kolmogorov differential systems

Hou, Zhanyuan (2023) On global dynamics of type-k competitive Kolmogorov differential systems. Nonlinearity, 36 (7). p. 3796. ISSN 0951-7715

[img] Text
Global dynamics of type-K competitive diff systems.pdf - Accepted Version
Restricted to Repository staff only until 13 June 2024.
Available under License Creative Commons Attribution Non-commercial No Derivatives 4.0.

Download (2MB) | Request a copy
Official URL: https://iopscience.iop.org/article/10.1088/1361-65...

Abstract / Description

This paper deals with global asymptotic behaviour of the dynamics for N-dimensional type-K competitive Kolmogorov systems of differential equations defined in the first orthant. It is known that the backward dynamics of such systems is type-K monotone. Assuming the system is dissipative and the origin is a repeller, it is proved that there exists a compact invariant set A which separates the basin of repulsion of the origin and the basin of repulsion of infinity and attracts all the non-trivial orbits. There are two closed sets SH and SV, their restriction to the interior of the first orthant are (N -1)-dimensional hypersurfaces, such that the asymptotic dynamics of the type-K system in the first orthant can be described by a system on either SH or SV: each trajectory in the interior of the first orthant is asymptotic to one in SH and one in SV. Geometric and asymptotic features of the global attractor A are investigated. It is proved that the partition A is divided into AH, A0 and AV such that AH, A0 are on SH and AV, A0 are on SV. Thus, A0 contains all the omega-limit sets for all interior trajectories of any type-K subsystems and the closure of the union of AH, AV as a subset of A is invariant and the upper boundary of the basin of repulsion of the origin. This A has the same asymptotic feature as the modified carrying simplex for a competitive system: every nontrivial trajectory below A is asymptotic to one in A and the omega-limit set is in A for every other nontrivial trajectory.

Item Type: Article
Additional Information: This is the Accepted Manuscript version of an article published in Nonlinearity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1361-6544/acda77
Uncontrolled Keywords: type-K competitive Kolmogorov systems, dynamics, type-K monotone, differential equations, first orthant
Subjects: 500 Natural Sciences and Mathematics
500 Natural Sciences and Mathematics > 510 Mathematics
500 Natural Sciences and Mathematics > 570 Life sciences; biology
Department: School of Computing and Digital Media
Depositing User: Zhanyuan Hou
Date Deposited: 12 Jun 2023 08:45
Last Modified: 22 Jan 2024 10:11
URI: https://repository.londonmet.ac.uk/id/eprint/8580

Actions (login required)

View Item View Item