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Nonlinear Feedback Shift Registers
Published in Haitao Li, Guodong Zhao, Peilian Guo, Zhenbin Liu, Analysis and Control of Finite-Value Systems, 2018
Haitao Li, Guodong Zhao, Peilian Guo, Zhenbin Liu
It is worth noting that the semi-tensor product of matrices has been successfully used in the study of FSRs [7,10–12]. In [10], a generalization of the linear feedback shift register synthesis problem was presented for synthesizing minimum-length matrix feedback shift registers to generate prescribed matrix sequences and so a new complexity measure, that is, matrix complexity, was introduced. [12] studied the stability of nonlinear feedback shift registers (NFSRs) using a Boolean network approach. A Boolean network is an autonomous system that evolves as an automaton through Boolean functions. A NFSR can be viewed as a Boolean network. Based on its Boolean network representation, some sufficient and necessary conditions are provided for globally (locally) stable NFSRs.
Process-based approach on tidal inlet evolution – Part 1
Published in C. Marjolein Dohmen-Janssen, Suzanne J.M.H. Hulscher, River, Coastal and Estuarine Morphodynamics: RCEM 2007, 2019
D.M.P.K. Dissanayake, J.A. Roelvink
To indicate the state of a system element, it is assigned an associated value 1 for ‘high’ and 0 for ‘low’. The future state of one element in the network depends on the states of the other elements in the network which are designated as that element’s inputs. The element may feedback its own state as a self-input. The state of an element in a Boolean network at a future time is governed by a logical rule or Boolean function, which operates on the element’s inputs. A detailed description of the Boolean approach for estuarine systems is given in Karunarathna & Reeve (2007).
Finite-time sampled-data set stabilisation of delayed probabilistic Boolean control networks
Published in International Journal of Systems Science, 2022
Boolean network is a special type of nonlinear systems with logical operations (Li & Wang, 2017; Wang et al., 2020; Zhong et al., 2014). The concept of Boolean networks was first proposed by Kauffman for the investigation of gene regulatory networks in Kauffman (1969). Furthermore, Boolean networks with input(s) and output(s) are called Boolean control networks (BCNs), which is a proper way to manipulate the dynamics of gene regulatory networks (Cheng, 2011). For the basic theory and applications of nonlinear systems with logical operations, please refer to Li and Lu (2020). Switched BCNs can be considered as a collection of BCNs with a switching signal (Yang et al., 2021). When the switching signal is independently and identically distributed, probabilistic BCNs can be obtained (Guo et al., 2019). In recent years, some fundamental results have been obtained for stochastic Boolean networks (Li et al., 2014; Zhu et al., 2020, 2022) and Markovian jump logical networks (Guo et al., 2019; Meng et al., 2017; Meng & Xiao, 2019). Markovian jump Boolean networks are more general than switched and probabilistic Boolean networks. However, it turns out to be more challenging to study Markovian jump BCNs due to the inherent high complexities of a combination of switching operations and stochastic properties. In Meng et al. (2019), a novel matrix was constructed to verify controllability of Markovian jump BCNs. As a class of factors affecting stability, time delays are common phenomenon, which are often encountered in the real world, such as communication system, chemical process and transportation system. For example, time delays are related to slow translocation, transcription and translation in gene regulatory networks (Meng et al., 2019). As we all know, even the inevitable small constant time delay in various cases may lead to poor system performance and instability. In addition, the existence of time delay brings difficulties and challenges to the analysis and control of delayed Boolean networks. Boolean network with time delay provides an unconventional perspective for the characteristics of complex systems (Ghil et al., 2008).