2,107 research outputs found
Qualitative analysis of solutions to mixed-order positive linear coupled systems with bounded or unbounded delays
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
Positivity of Continuous-Time Descriptor Systems With Time Delays
This technical note is concerned with positivity characteristic of continuous-time descriptor systems with time delays. First, a set of necessary and sufficient conditions is presented to check the property. Then, considering a descriptor time-delay system with two assumptions, a new time-delay system is established whose positivity is equivalent to that of the original system. Furthermore, a set of necessary and sufficient conditions is provided to check the positivity of the new system. Finally, a numerical example is given to illustrate the validity of the results obtained
Time-delayed models of gene regulatory networks
We discuss different mathematical models of gene regulatory networks as relevant to the onset and development of cancer. After discussion of alternativemodelling approaches, we use a paradigmatic two-gene network to focus on the role played by time delays in the dynamics of gene regulatory networks. We contrast the dynamics of the reduced model arising in the limit of fast mRNA dynamics with that of the full model. The review concludes with the discussion of some open problems
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