Non-Oscillation Principle for Eventually Competitive and Cooperative Systems

Lin Niu; Yi Wang

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arXiv · 1809.10068

Non-Oscillation Principle for Eventually Competitive and Cooperative Systems

Lin Niu·Yi Wang

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Abstract

A nonlinear dynamical system is called eventually competitive (or cooperative) provided that it preserves a partial order in backward (or forward) time only after some reasonable initial transient. We presented in this paper the Non-oscillation Principle for eventually competitive or cooperative systems, by which the non-ordering of (both $\omega$- and $\alpha$-) limit sets is obtained for such systems; and moreover, we established the Poincar\'{e}-Bendixson Theorem and structural stability for three-dimensional eventually competitive and cooperative systems.

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Lin Niu, Yi Wang. 2018-09-26. Non-Oscillation Principle for Eventually Competitive and Cooperative Systems. https://arxiv.org/abs/1809.10068

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