论文标题
定性分析具有有界或无限延迟的混合顺序正线性耦合系统的解决方案
Qualitative analysis of solutions to mixed-order positive linear coupled systems with bounded or unbounded delays
论文作者
论文摘要
本文讨论了具有有限或无限延迟的混合顺序正线性耦合系统的定性理论。首先，我们介绍了与时变延迟的混合阶线性耦合系统的解决方案的存在和独特性的一般结果。接下来，我们获得了必要和充分的标准，该标准表征了混合顺序延迟线性耦合系统的阳性。我们的主要贡献是在第5节中。更确切地说，通过将解决方案的平滑度用于分数微分方程，并为混合订购延迟阳性系统的解决方案开发了新的适当比较原理，我们证明了混合级非均匀的线性线性正相的吸引力，并具有有界或没有结合的延迟。我们还建立了一个必要且充分的条件，以表征同质系统的稳定性。由于这些结果，我们展示了解决混合延迟延迟非均匀线性正耦合系统的最小渐近界限，其中干扰是连续和界限的。最后，我们提供数值模拟来说明提出的理论结果。
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.
