Structural stability analysis of gene regulatory networks modeled by Boolean networks

Liang, Shuang; Zhao, Guodong; Li, Haitao; Ding, Xueying

doi:10.1002/mma.5488

Cited by 22 publications

(11 citation statements)

References 35 publications

(50 reference statements)

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“…With the rapid development of control theory, the problem of controllability for a special kind of logical control networks, Boolean control networks, was also investigated by researchers. For more details of the recent works in this regard, we refer readers to [36][37][38]. Controllability is one of the fundamental concepts in mathematical control theory.…”

Section: Introductionmentioning

confidence: 99%

New Results on Controllability for a Class of Fractional Integrodifferential Dynamical Systems with Delay in Banach Spaces

Deng-feng

2021

Fractal Fract

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The present work addresses some new controllability results for a class of fractional integrodifferential dynamical systems with a delay in Banach spaces. Under the new definition of controllability , first introduced by us, we obtain some sufficient conditions of controllability for the considered dynamic systems. To conquer the difficulties arising from time delay, we also introduce a suitable delay item in a special complete space. In this work, a nonlinear item is not assumed to have Lipschitz continuity or other growth hypotheses compared with most existing articles. Our main tools are resolvent operator theory and fixed point theory. At last, an example is presented to explain our abstract conclusions.

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Section: Introductionmentioning

confidence: 99%

New Results on Controllability for a Class of Fractional Integrodifferential Dynamical Systems with Delay in Banach Spaces

Deng-feng

2021

Fractal Fract

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“…We point out that complete controllability of infinite dimensional systems with noncompact semigroup is an important research direction, and there have been many outstanding achievements in this regard such as [21][22][23][24][25][26]. For more details of other research results on control theory, please refer to [27][28][29][30][31][32][33][34][35][36][37][38][39][40] and the reference therein.…”

Section: Introductionmentioning

confidence: 99%

New Controllability Results of Fractional Nonlocal Semilinear Evolution Systems with Finite Delay

Deng-feng

Mao

2020

Complexity

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In the present paper, sufficient conditions ensuring the complete controllability for a class of semilinear fractional nonlocal evolution systems with finite delay in Banach spaces are derived. The new results are obtained under a weaker definition of complete controllability we introduced, and then the Lipschitz continuity and other growth conditions for the nonlinearity and nonlocal item are not required in comparison with the existing literatures. In addition, an appropriate complete space and a corresponding time delay item are introduced to conquer the difficulties caused by time delay. Our main tools are properties of resolvent operators, theory of measure of noncompactness, and Mönch fixed point theorem.

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“…Furthermore, we need to find all the fixed points and cycles when we are analyzing the stability for BNs. Many great results have been reached . Meng et al studied BNs with Markovian jump parameters.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of activation‐inhibition Boolean networks with stochastic function structures

Zhao

Liang

2020

Math Methods in App Sciences

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This paper analyzes the stability of activation‐inhibition Boolean networks with stochastic function structures. First, the activation‐inhibition Boolean networks with stochastic function structures are converted to the form of logical networks by the method of semitensor product of matrices. Second, based on the obtained algebraic forms, we use matrices to denote the index set of possible logical operators and transition probabilities for activation‐inhibition Boolean networks. Third, equivalence criterions are presented for the stabilities analysis of activation‐inhibition Boolean networks with stochastic function structures. Finally, an example is given to verify the validity of the results.

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Structural stability analysis of gene regulatory networks modeled by Boolean networks

Cited by 22 publications

References 35 publications

New Results on Controllability for a Class of Fractional Integrodifferential Dynamical Systems with Delay in Banach Spaces

New Results on Controllability for a Class of Fractional Integrodifferential Dynamical Systems with Delay in Banach Spaces

New Controllability Results of Fractional Nonlocal Semilinear Evolution Systems with Finite Delay

Stability analysis of activation‐inhibition Boolean networks with stochastic function structures

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