Lyapunov stability of generalized ribosome flows*

Vághy, Mihály A.; Szederkényi, Gábor

doi:10.1016/j.ifacol.2022.08.030

Cited by 2 publications

(2 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An arbitrary directed graph structure of such models with general time-invariant kinetics was considered in [27], where the existence and uniqueness of equlibria, persistence and contractivity (non-expansive property) of the solutions was shown using the theory of Petri nets, compartmental systems, and earlier results on RFMs. The stability of this model class with logarithmic Lyapunov functions was shown in [28], while a port-Hamiltonian description was given in [29].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Persistence and stability of generalized ribosome flow models with time-varying transition rates

Vághy

Szederkényi

2023

PLoS ONE

Self Cite

View full text Add to dashboard Cite

In this paper some important qualitative dynamical properties of generalized ribosome flow models are studied. Ribosome flow models known from the literature are generalized by allowing an arbitrary directed network structure between compartments, and by assuming general time-varying rate functions corresponding to the transitions. Persistence of the dynamics is shown using the chemical reaction network (CRN) representation of the system where the state variables correspond to ribosome density and the amount of free space in the compartments. The L1 contractivity of solutions is also proved in the case of periodic reaction rates having the same period. Further we prove the stability of different compartmental structures including strongly connected ones with entropy-like logarithmic Lyapunov functions through embedding the model into a weakly reversible CRN with time-varying reaction rates in a reduced state space. Moreover, it is shown that different Lyapunov functions may be assigned to the same model depending on the non-unique factorization of the reaction rates. The results are illustrated through several examples with biological meaning including the classical ribosome flow model on a ring.

show abstract

Section: Introductionmentioning

confidence: 99%

“…Based on the above overview, the aim of this paper is to extend the results of [27,28] in the following respects: considering even more general kinetics with explicit time-dependence, the qualitative analysis of periodic solutions, and finally, stability analysis with a family of different logarithmic Lyapunov functions.…”

Section: Introductionmentioning

confidence: 99%