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arXiv · 2208.10706

Qualitative analysis of solutions to mixed-order positive linear coupled systems with bounded or unbounded delays

H. T. Tuan·L. V. Thinh
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Abstract

This paper addresses the qualitative theory of mixed-order positive linear coupled systems with bounded or unbounded delays. First, we introduce a general result on the existence and uniqueness of solutions to mixed-order linear coupled systems with time-varying delays. Next, we obtain the necessary and sufficient criteria which characterize the positivity of a mixed-order delay linear coupled system. Our main contribution is in Section 5. More precisely, by using a smoothness property of solutions to fractional differential equations and developing a new appropriated comparison principle for solutions to mixed-order delayed positive systems, we prove the attractivity of mixed-order non-homogeneous linear positive coupled systems with bounded or unbounded delays. We also establish a necessary and sufficient condition to characterize the stability of homogeneous systems. As a consequence of these results, we show the smallest asymptotic bound of solutions to mixed-order delay non-homogeneous linear positive coupled systems where disturbances are continuous and bounded. Finally, we provide numerical simulations to illustrate the proposed theoretical results.

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H. T. Tuan, L. V. Thinh. 2023-08-13. Qualitative analysis of solutions to mixed-order positive linear coupled systems with bounded or unbounded delays. https://doi.org/10.1051/cocv%2F2023057

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