Persistence In Chemical Reaction Networks With Arbitrary Time Delays

Komatsu, Hirokazu; Nakajima, Hiroyuki

doi:10.1137/18m117265x

Cited by 12 publications

(7 citation statements)

References 14 publications

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“…Anderson et al [2,5] further proved that the ω-limit point, i.e., any element in ω(x 0 ), can only exist in the face of the stoichiometric compatibility class of x 0 , i.e., Q W ∩P x 0 , when W is a semilocking set. This result also applies to DeMASs [21], i.e., the ω-limit point in ω(ψ) can only exist in L W ∩ D ψ in the case that W is a semilocking set. It is expected that the ω-limit set theorem also holds for DeCBMASs.…”

Section: ω-Limit Set Theorem Of Demassmentioning

confidence: 81%

“…The equilibrium and complex balanced equilibrium in a DeMAS share the same definitions as those in a MAS [21], i.e., following 2.4. We call a DeMAS having a complex balanced equilibrium a delayed complex balanced mass-action system (DeCBMAS).…”

Section: Demassmentioning

confidence: 99%

“…[22] reveals the semistability of a complex balanced system with time delay. The first research on the persistence of the time-delayed system is in [21] by Hirokazu Komatsu and Hiroyuki Nakajima which is a natural extension of the results in [5,6]. This paper focuses on the persistence property of two kinds of time-delayed complex balanced systems.…”

Section: Introductionmentioning

confidence: 97%

See 2 more Smart Citations

Persistence of Delayed Complex Balanced Chemical Reaction Networks

Zhang¹,

Gao²

2019

Preprint

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Time delay is a very common phenomenon in real biological or industrial systems. This paper studies the persistence of complex balanced mass action systems with any constant time delays(DeMAS). We give several sufficient conditions for DeMASs to be persistent based on the dimension of intersection of stoichiometric compatibility class and R n ≥0 . These results are analogous to the theorems which have proven by Anderson in [2] and [4] for the non-delayed mass action system. Besides, persistence implies global asymptotic stability for complex balanced DeMASs which means that all trajectories starting at a positive concentration trend to the unique positive constant equilibrium in its stoichiometric compatibility class. From this paper, we can learn further about the long-term property of the delayed complex balanced system.

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Section: ω-Limit Set Theorem Of Demassmentioning

confidence: 81%

Section: Demassmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

See 1 more Smart Citation

Persistence of Delayed Complex Balanced Chemical Reaction Networks

Zhang¹,

Gao²

2019

Preprint

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“…By using the similar proof as Lemma 4.5 in [ [13]], we can also obtain that ψ ∈ ∂ C+ in one ω-limit set must have the form:…”

Section: Quantification Of Stoichiometric Compatibility Classes In De...mentioning

confidence: 82%

“…Proof. The uniqueness of equilibrium in each stoichiometric compatibility class is already derived in [13].…”

Section: Quantification Of Stoichiometric Compatibility Classes In De...mentioning

confidence: 99%

Some dynamical properties of delayed weakly reversible mass-action systems

Zhang

Gao

2019

Preprint

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This paper focuses on the dynamical properties of delayed complex balanced systems. We first study the relationship between the stoichiometric compatibility classes of delayed and nondelayed systems. Using this relation we give another way to derive the existence of positive equilibrium in each stoichiometric compatibility class for delayed complex balanced systems. And if time delays are constant, the result can be generalized to weakly reversible networks. Also, by utilizing the Lyapunov-Krasovskii functional, we can obtain a long-time dynamical property about ω-limit set of the complex balanced system with constant time delays. An example is also provided to support our results.

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Stability analysis for Butlerov chemical reaction in batch reactor

Komatsu

Yokota

2022

J Math Chem

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Persistence In Chemical Reaction Networks With Arbitrary Time Delays

Cited by 12 publications

References 14 publications

Persistence of Delayed Complex Balanced Chemical Reaction Networks

Persistence of Delayed Complex Balanced Chemical Reaction Networks

Some dynamical properties of delayed weakly reversible mass-action systems

Stability analysis for Butlerov chemical reaction in batch reactor

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