Mean square exponential stability for stochastic memristor-based neural networks with leakage delay

Wang, Fen; Chen, Yuanlong

doi:10.1016/j.chaos.2021.110811

Cited by 13 publications

(4 citation statements)

References 44 publications

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“…Importantly, because of the overlapping of evolutionary and ecological timescales within microbiomes, the community matrix, is in principle, also influenced by intra-species diversity, but to what extent remains poorly understood [11][12][13][14]34 . A species rarely exists as a homogenous population due to spatial partitioning and genomic variation from pre-existing or de novo mutations 35 .…”

Section: Mainmentioning

confidence: 99%

“…Despite the prevalence of intra-species variation (ISV) in nature, how ISV affects the community matrix is not fully known. Indeed, the role of ISV on community composition and stability has rarely been tested experimentally [11][12][13]33,[36][37][38][39] . Some theoretical studies have also yielded contradictory results regarding the role of intraspecific variation on species coexistence 14 .…”

Section: Mainmentioning

confidence: 99%

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Quantifying the intra- and inter-species community interaction in a microbiome by dynamic covariance mapping

Serohijos,

Gencel,

Hui

et al. 2024

Preprint

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A microbiome’s composition, stability, and response to perturbations is dictated by the community interaction matrix 1-10 that is commonly assayed by pair-wise species competition. In their natural environment however, microbes concurrently experience multiple species, face conditions that may be difficult to mimic in vitro, and have members that are impractical to isolate. Additionally, due to overlapping of evolutionary and ecological timescales, the community interaction matrix is also influenced by intra-species diversity, but how and to what extent remains poorly understood 11-14. Here, we develop a general approach called Dynamic Covariance Mapping (DCM) to estimate the interaction matrix of multispecies microbiome community in its natural environment from abundance time-series data. Together with intra-species high-resolution lineage tracking via chromosomal barcoding, we quantify the inter- and intra-species community interaction matrix during E. coli colonization of mice gut microbiome with increasing complexity: germ-free, antibiotic-perturbed, and innate microbiota. With DCM, we differentiate three temporal phases of invasion in the susceptible communities: 1) initial loss of community stability as E. coli enters; 2) recolonization of some gut bacteria; and 3) recovery of stability with E. coli clones coexisting with resident bacteria in a quasi-steady state. These phases are influenced by specific interactions between E. coli sub-lineages with other species in the community. These results highlight the transient nature and time-dependence of community interaction networks in microbiomes driven by the persistent coupling of ecological and evolutionary dynamics. Our theoretical and experimental approach can be applied to characterize coupled ecological-evolutionary dynamics of bacterial communities in vitro and in situ.

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Section: Mainmentioning

confidence: 99%

Section: Mainmentioning

confidence: 99%

Quantifying the intra- and inter-species community interaction in a microbiome by dynamic covariance mapping

Serohijos,

Gencel,

Hui

et al. 2024

Preprint

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“…In order to realize the control target more accurately, it is necessary to consider stochastic disturbance in system dynamics. Therefore, SMNNs modeled by

\mathrm{It}\hat{\mathrm{o}}

stochastic differential equation 27,28 are investigated in this paper. It is worth noting that the above mentioned ETIC strategies for deterministic systems cannot be directly applied to SMNNs.…”

Section: Introductionmentioning

confidence: 99%

Synchronization of stochastic memristive neural networks via event‐triggered impulsive control

Zhang,

Mu,

2023

Adaptive Control & Signal

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This paper investigates the synchronization problem for master‐slave stochastic memristive neural networks (SMNNs) with time‐delay via event‐triggered impulsive control (ETIC). Firstly, a novel ETIC method is designed for SMNNs to realize quasi‐synchronization in mean square sense. Different from time‐triggered impulsive control (TTIC) in the existing results on SMNNs, the proposed event‐triggered method determines impulsive instants based on the real‐time system states, which can reduce redundant impulses. Compared with the existing ETIC for deterministic memristive neural networks (MNNs), the proposed event‐triggered mechanism (ETM) can exclude Zeno behavior completely by adding the waiting time, when stochastic disturbances occur in MNNs. Secondly, if the master SMNNs have nonzero control inputs, an adaptive‐impulsive hybrid controller with ETM is designed to realize almost surely exponential synchronization. Under the ETM, the number of transmitted events is reduced, then control resources can be saved. Zeno behavior can be excluded in almost sure sense. Ultimately, simulations are presented to illustrate the validity of the obtained results.

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“…The resistance of memristor changes continuously with the flow of current, so memristor can be used in analog circuits. It is this characteristic of memristor that makes its application become a research hotspot [2][3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Aperiodically Intermittent Control Strategy and Adaptive Synchronization of Neural Networks With Inertial and Memristive Terms

Liu,

Wang,

Jiang

et al. 2023

IEEE Access

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The problem of adaptive aperiodic intermittent synchronization scheme is studied for inertial memristive delayed neural networks by using a piecewise Lyapunov function in this article. First, a appropriate two-parameter variable replace technique is proposed about the second-order differential equation, and inertial memristive delayed neural systems can be replaced by first-order derivatives of states. Second, an aperiodic intermittent control strategy which can be degenerated periodically intermittent controller or continue feedback controller is designed. Third, by building a piecewise Lyapunov function and using piecewise analytical skills, a number of novel and effective norms to guarantee the exponential synchronization and global exponential synchronization of memristive delayed inertial systems are obtained. Besides, an adaptive control method is proposed to adjust control gains. And asymptotic synchronization and exponential synchronization are ensured by constructing of Lyapunov functional. In the end, simulation results are given to support the significance of the research work.

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Mean square exponential stability for stochastic memristor-based neural networks with leakage delay

Cited by 13 publications

References 44 publications

Quantifying the intra- and inter-species community interaction in a microbiome by dynamic covariance mapping

Quantifying the intra- and inter-species community interaction in a microbiome by dynamic covariance mapping

Synchronization of stochastic memristive neural networks via event‐triggered impulsive control

Aperiodically Intermittent Control Strategy and Adaptive Synchronization of Neural Networks With Inertial and Memristive Terms

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