On global dynamics of type-k competitive Kolmogorov differential systems

Hou, Zhanyuan (2023) On global dynamics of type-k competitive Kolmogorov differential systems. Nonlinearity. ISSN 0951-7715 (In Press)

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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
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:	12 Jun 2023 08:45
URI:	https://repository.londonmet.ac.uk/id/eprint/8580

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