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Xie KY, Zhang CK, Lee S, He Y, Liu Y. Delay-dependent Lurie-Postnikov type Lyapunov-Krasovskii functionals for stability analysis of discrete-time delayed neural networks. Neural Netw 2024; 173:106195. [PMID: 38394998 DOI: 10.1016/j.neunet.2024.106195] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2023] [Revised: 01/18/2024] [Accepted: 02/18/2024] [Indexed: 02/25/2024]
Abstract
This paper addresses the influence of time-varying delay and nonlinear activation functions with sector restrictions on the stability of discrete-time neural networks. Compared to previous works that mainly focuses on the influence of delay information, this paper devotes to activation nonlinear functions information to help compensate the analysis technique based on Lyapunov-Krasovskii functional (LKF). A class of delay-dependent Lurie-Postnikov type integral terms involving sector constraints of nonlinear activation function is proposed to complement the LKF construction. The less conservative criteria for the stability analysis of discrete-time delayed networks is given by using improved LKF. Numerical examples show that conservatism can be reduced by the delay-dependent integral terms involving nonlinear activation functions.
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Affiliation(s)
- Ke-You Xie
- School of Automation, China University of Geosciences, Wuhan 430074, China; Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, Wuhan 430074, China; Engineering Research Center of Intelligent Technology for Geo-Exploration, Ministry of Education, Wuhan 430074, China
| | - Chuan-Ke Zhang
- School of Automation, China University of Geosciences, Wuhan 430074, China; Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, Wuhan 430074, China; Engineering Research Center of Intelligent Technology for Geo-Exploration, Ministry of Education, Wuhan 430074, China
| | - Sangmoon Lee
- School of Electronic and Electrical Engineering, Kyungpook National University, Daegu 41566, South Korea.
| | - Yong He
- School of Automation, China University of Geosciences, Wuhan 430074, China; Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, Wuhan 430074, China; Engineering Research Center of Intelligent Technology for Geo-Exploration, Ministry of Education, Wuhan 430074, China
| | - Yajuan Liu
- School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China
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2
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Global Stability of Delayed Genetic Regulatory Networks with Wider Hill Functions: A Mixing Monotone Semiflows Approach. Neurocomputing 2023. [DOI: 10.1016/j.neucom.2023.01.057] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
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3
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Song X, Li X, Song S, Ahn CK. State Observer Design of Coupled Genetic Regulatory Networks With Reaction-Diffusion Terms via Time-Space Sampled-Data Communications. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2022; 19:3704-3714. [PMID: 34550890 DOI: 10.1109/tcbb.2021.3114405] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
In this paper, state observation of coupled reaction-diffusion genetic regulatory networks (GRNs) with time-varying delays is investigated under Dirichlet boundary conditions. First, the above GRNs are constructed to model gene regulatory properties, where the feedback regulation function of the GRNs is assumed to exhibit the Hill form and a novel method to deal with it is introduced. Then a time-space sampled-data state observer is designed for the mentioned networks and new criteria are established by utilizing the Lyapunov stability theory and the inequality techniques of Halanay et al. Finally, the validity of the theoretical results is proved by numerical examples.
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4
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Novel global exponential stability results for a class of two-coupled-hub nonlinear genetic regulatory networks with time-varying delays. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2022.08.063] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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5
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Ling G, Liu X, Guan ZH, Ge MF, Tong YH. Input-to-state stability for switched stochastic nonlinear systems with mode-dependent random impulses. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2022.03.034] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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6
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New Results on Global Exponential Stability of Genetic Regulatory Networks with Diffusion Effect and Time-Varying Hybrid Delays. Neural Process Lett 2021. [DOI: 10.1007/s11063-021-10573-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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7
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Ling G, Ge MF, Liu X, Xiao G, Fan Q. Stochastic quasi-synchronization of heterogeneous delayed impulsive dynamical networks via single impulsive control. Neural Netw 2021; 139:223-236. [PMID: 33794425 DOI: 10.1016/j.neunet.2021.03.011] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2020] [Revised: 03/02/2021] [Accepted: 03/08/2021] [Indexed: 10/21/2022]
Abstract
This paper investigates the quasi-synchronization problem of the stochastic heterogeneous complex dynamical networks with impulsive couplings and multiple time-varying delays. It is shown that this kind of dynamical networks can achieve exponential quasi-synchronization by exerting impulsive control added on only one chosen pinning node. By employing the Lyapunov stability theory, some sufficient criteria on quasi-synchronization for this dynamical network are established, revealing the relationship between the quasi-synchronization performance and the stochastic perturbations as well as the frequency and strength of impulsive coupling. Finally, some numerical examples are used to illustrate the effectiveness of the main results.
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Affiliation(s)
- Guang Ling
- School of Science, Wuhan University of Technology, Wuhan 430070, China
| | - Ming-Feng Ge
- School of Mechanical Engineering and Electronic Information, China University of Geosciences, Wuhan 430074, China.
| | - Xinghua Liu
- School of Electrical Engineering, Xi'an University of Technology, Xi'an 710048, China
| | - Gaoxi Xiao
- School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore
| | - Qingju Fan
- School of Science, Wuhan University of Technology, Wuhan 430070, China
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Ling G, Ge MF, Tong YH, Fan Q. Exponential Synchronization of Delayed Switching Genetic Oscillator Networks via Mode-Dependent Partial Impulsive Control. Neural Process Lett 2021. [DOI: 10.1007/s11063-021-10488-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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9
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Duddu AS, Sahoo S, Hati S, Jhunjhunwala S, Jolly MK. Multi-stability in cellular differentiation enabled by a network of three mutually repressing master regulators. J R Soc Interface 2020; 17:20200631. [PMID: 32993428 DOI: 10.1098/rsif.2020.0631] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
Identifying the design principles of complex regulatory networks driving cellular decision-making remains essential to decode embryonic development as well as enhance cellular reprogramming. A well-studied network motif involved in cellular decision-making is a toggle switch-a set of two opposing transcription factors A and B, each of which is a master regulator of a specific cell fate and can inhibit the activity of the other. A toggle switch can lead to two possible states-(high A, low B) and (low A, high B)-and drives the 'either-or' choice between these two cell fates for a common progenitor cell. However, the principles of coupled toggle switches remain unclear. Here, we investigate the dynamics of three master regulators A, B and C inhibiting each other, thus forming three-coupled toggle switches to form a toggle triad. Our simulations show that this toggle triad can lead to co-existence of cells into three differentiated 'single positive' phenotypes-(high A, low B, low C), (low A, high B, low C) and (low A, low B, high C). Moreover, the hybrid or 'double positive' phenotypes-(high A, high B, low C), (low A, high B, high C) and (high A, low B, high C)-can coexist together with 'single positive' phenotypes. Including self-activation loops on A, B and C can increase the frequency of 'double positive' states. Finally, we apply our results to understand cellular decision-making in terms of differentiation of naive CD4+ T cells into Th1, Th2 and Th17 states, where hybrid Th1/Th2 and hybrid Th1/Th17 cells have been reported in addition to the Th1, Th2 and Th17 ones. Our results offer novel insights into the design principles of a multi-stable network topology and provide a framework for synthetic biology to design tristable systems.
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Affiliation(s)
- Atchuta Srinivas Duddu
- Centre for BioSystems Science and Engineering, Indian Institute of Science, Bangalore, India
| | - Sarthak Sahoo
- Centre for BioSystems Science and Engineering, Indian Institute of Science, Bangalore, India.,UG Programme, Indian Institute of Science, Bangalore, India
| | - Souvadra Hati
- UG Programme, Indian Institute of Science, Bangalore, India
| | - Siddharth Jhunjhunwala
- Centre for BioSystems Science and Engineering, Indian Institute of Science, Bangalore, India
| | - Mohit Kumar Jolly
- Centre for BioSystems Science and Engineering, Indian Institute of Science, Bangalore, India
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Reachable set estimation for genetic regulatory networks with time-varying delays and bounded disturbances. Neurocomputing 2020. [DOI: 10.1016/j.neucom.2020.03.113] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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Zhang L, Zhang X, Xue Y, Zhang X. New Method to Global Exponential Stability Analysis for Switched Genetic Regulatory Networks With Mixed Delays. IEEE Trans Nanobioscience 2020; 19:308-314. [PMID: 32070989 DOI: 10.1109/tnb.2020.2971548] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
In this paper, the sufficient conditions for the global exponential stability of the switched genetic regulatory networks with mixed time delays are obtained. The proposed method does not need the construction of Lyapunov-Krasovskii functional, but is directly proceeded by the definition of global exponential stability. The derived sufficient conditions can easily be verified by checking the eigenvalues of a constant matrix or solving several simple linear matrix inequalities. Finally, two numerical examples are presented to illustrate that the obtained global exponential stability criteria are available.
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12
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Xiao M, Zheng WX, Jiang G. Bifurcation and Oscillatory Dynamics of Delayed Cyclic Gene Networks Including Small RNAs. IEEE TRANSACTIONS ON CYBERNETICS 2019; 49:883-896. [PMID: 29994187 DOI: 10.1109/tcyb.2017.2789331] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
It has been demonstrated in a large number of experimental results that small RNAs (sRNAs) play a vital role in gene regulation processes. Thus, the gene regulation process is dominated by sRNAs in addition to messenger RNAs and proteins. However, the regulation mechanism of sRNAs is not well understood and there are few models considering the effect of sRNAs. So it is of realistic biological background to include sRNAs when modeling gene networks. In this paper, sRNAs are incorporated into the process of gene expression and a new differential equation model is put forward to describe cyclic genetic regulatory networks with sRNAs and multiple delays. We mainly investigate the stability and bifurcation criteria for two cases: 1) positive cyclic genetic regulatory networks and 2) negative cyclic genetic regulatory networks. For a positive cyclic genetic regulatory network, it is revealed that there may exist more than one equilibrium and the multistability can appear. Sufficient conditions are established for the delay-independent stability and fold bifurcations. It is found that the dynamics of positive cyclic gene networks has no bearing on time delays, but depends on the biochemical parameters, the Hill coefficient and the equilibrium itself. For a negative cyclic genetic regulatory network, it is proved that there exists a unique equilibrium. Delay-dependent conditions for the stability are derived, and the existence of Hopf bifurcations is examined. Different from the delay-independent stability of positive gain networks, the stability of equilibrium is determined not only by the biochemical parameters, the Hill coefficient and the equilibrium itself, but also by the total delay. At last, three illustrative examples are provided to validate the major results.
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He DX, Ling G, Guan ZH, Hu B, Liao RQ. Multisynchronization of Coupled Heterogeneous Genetic Oscillator Networks via Partial Impulsive Control. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2018; 29:335-342. [PMID: 27875233 DOI: 10.1109/tnnls.2016.2619907] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
This paper focuses on the collective dynamics of multisynchronization among heterogeneous genetic oscillators under a partial impulsive control strategy. The coupled nonidentical genetic oscillators are modeled by differential equations with uncertainties. The definition of multisynchronization is proposed to describe some more general synchronization behaviors in the real. Considering that each genetic oscillator consists of a large number of biochemical molecules, we design a more manageable impulsive strategy for dynamic networks to achieve multisynchronization. Not all the molecules but only a small fraction of them in each genetic oscillator are controlled at each impulsive instant. Theoretical analysis of multisynchronization is carried out by the control theory approach, and a sufficient condition of partial impulsive controller for multisynchronization with given error bounds is established. At last, numerical simulations are exploited to demonstrate the effectiveness of our results.
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14
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Zou C, Wei X, Zhang Q, Zhou C. Passivity of Reaction–Diffusion Genetic Regulatory Networks with Time-Varying Delays. Neural Process Lett 2017. [DOI: 10.1007/s11063-017-9682-7] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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15
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Ling G, Guan ZH, Hu B, Lai Q, Wu Y. Multistability and Bifurcation Analysis of Inhibitory Coupled Cyclic Genetic Regulatory Networks With Delays. IEEE Trans Nanobioscience 2017; 16:216-225. [PMID: 28212091 DOI: 10.1109/tnb.2017.2669112] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
Many biological systems have the conspicuous property to present more than one stable state and diverse rhythmic behaviors. A closed relationship between these complex dynamic behaviors and cyclic genetic structures has been witnessed by pioneering works. In this paper, a typical structure of inhibitory coupled cyclic genetic networks is introduced to further enlighten this mechanism of stability and biological rhythms of living cells. The coupled networks consist of two identical cyclic genetic subnetworks, which inhibit each other directly. Each subnetwork can be regarded as a genetic unit at the cellular level. Multiple time delays, including both internal and coupling delays, are considered. The existence of positive equilibriums for this kind of coupled systems is proved, and the stability for each equilibrium is analyzed without or with delays. It is shown that the coupled networks with positive cyclic genetic units have an ability to show multistability, while the coupled networks with negative units may present a series of Hopf bifurcations with the variation of time delays. Several numerical simulations are made to prove our results.
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Zhu Z, Zhu Y, Zhang L, Al-Yami M, Abouelmagd E, Ahmad B. Mode-mismatched estimator design for Markov jump genetic regulatory networks with random time delays. Neurocomputing 2015. [DOI: 10.1016/j.neucom.2015.05.011] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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