查看更多>>摘要：? 2022The number of subtrees, also referred to as the subtrees index, is a key parameter to measure graph structures such as networks. In this paper, we investigate the number of subtrees of planar two-tree networks. By “adding a virtual edge” and “edge orientation”, we present a linear time algorithm for computing the number of subtrees of planar two-tree networks, as well as a family of planar two-connected networks. As applications, we provide the formulae for the number of subtrees of the famous small-world Farey network and GDURT network. We also discuss the relationship between the spanning subtree number and the subtree number of these networks.
查看更多>>摘要：? 2022 The Author(s)The paper presents a new definition of nabla fractional-order difference, equivalent to the Grünwald-Letnikov difference. The difference is based on the general approach of orthonormal basis functions in terms of discrete-time Takenaka-Malmquist filters. The main advantage of the proposed definition is that for finite model length, the model quickly converges to the actual difference. The paper proposes the method of selecting the poles of the Takenaka-Malmquist functions. It also proposes the implementation of the Takenaka-Malmquist-based difference in non-commensurate state-space system and fractional-order integrator. Simulation experiments show the proposed methodology's high effectiveness in modeling fractional-order difference, integrator, and non-commensurate state-space systems.
查看更多>>摘要：? 2022 Elsevier Inc.Vegetation pattern can describe spatial feature of vegetation in arid ecosystem. Soil-water diffusion is of vital importance in spatial structures of vegetation, which is not comprehensively understood. In this thesis, we reveal the impact of soil-water diffusion on vegetation patterns through steady-state bifurcation analysis. The result indicates that if soil-water diffusion coefficient is appropriately large, there is at least one non-constant steady-state solution to a spatial vegetation system. Moreover, with the aid of Crandall-Rabinowitz bifurcation theorem and implicit function theorem, local structure of non-constant steady-state solutions is obtained. Subsequently, the global continuation of the local steady-state bifurcation is performed, and we get global structure of non-constant solution. At last, the above non-constant steady-state solution is illustrated by our numerical simulations. The extended simulation additionally shows that the spatial heterogeneity of species is enhanced gradually as soil-water diffusion increases.
查看更多>>摘要：? 2022In recent years, grad-div stabilization has become a popular technique for improving the mass conservation of a solution to the incompressible Navier-Stokes equations (NSE). Grad-div stabilization can be easily implemented in any code that already uses the very common Taylor-Hood finite elements. In this paper we do a close review of the grad-div stabilized and modular grad-div stabilized NSE applied to a well-known benchmark problem: 2D flow around a cylindrical obstacle. We show that using current methods grad-div stabilization can change the calculated drag and lift coefficients. We will then suggest a remedy for the given test problem and verify our results by showing the grad-div parameters agree with the reference values and those calculated using Scott-Vogelius finite elements.
查看更多>>摘要：? 2022This paper aims to design a robust observer-based dissipative controller for discrete-time Takagi–Sugeno (T-S) fuzzy systems with nonhomogeneous Markov jumps through a non-parallel distributed compensation (non-PDC) scheme. Based on a mode-dependent nonquadratic Lyapunov function, the final form of the stabilization conditions is expressed as linear matrix inequalities in a less conservative manner. To be specific, this paper proposes a decoupling technique that can address the inherent nonconvex terms by extracting them from the stabilization conditions, where all slack variables are set to be fuzzy-basis-dependent for less conservative performance. Furthermore, the proposed stabilization method adopts a one-step design strategy that simultaneously designs the fuzzy observer and control gains without any iteration procedures by employing a positive tuning parameter. In particular, the time-varying transition probabilities included in the stabilization conditions are effectively removed using a modified relaxation technique that can avoid excessive use of free weighting matrices. Finally, based on four examples, the validity of the proposed method is verified through comparison with other studies.
查看更多>>摘要：? 2022 Elsevier Inc.Recent studies have shown that higher-order interactions have a vital role in exploring the collective dynamics of the networks. In particular, the collective behavior of a network of neuron models with many-body interactions has received much attention among researchers in recent times. In this paper, we study the effect of higher-order interactions in the synchronization stability of the network of neuron models, namely Hindmarsh-Rose and Morris-Lecar models, with electromagnetic induction. We consider both two-body and three-body interactions to be diffusive and analyze their effect on the synchronization of the network of neurons. Our analysis shows that higher-order interactions can make the neurons synchrony with the minimal value of first-order coupling strengths in both neuron models. Besides, electromagnetic flux coupling strength also has a significant effect on the synchronization of neurons. In the Hindmarsh-Rose neuron model, the flux coupling demands higher coupling strength in both the first and second-order interactions for the synchronization of neurons. However, the Morris-Lecar neuron model shows a notable distinct effect, where the flux coupling enhances the synchronization of neurons with lesser first and second-order coupling strengths.
查看更多>>摘要：? 2022This paper presents a backstepping control for a class of single-input-single-output (SISO) strict-feedback fractional discrete-time systems for the first time. By tracking state variables in error functions, the stability criterion is used to design a controller such that the closed-loop system is stable. Finally, two simulation examples are demonstrated. By using different fractional order parameters, the fractional discrete-time system is stable and the effectiveness of the proposed controller is verified.
查看更多>>摘要：? 2022This work aims at obtaining a numerical approximation to the solution of a two-parameter singularly perturbed convection-diffusion-reaction system of partial differential equations with discontinuous coefficients. This discontinuity, together with small values of the perturbation parameters, causes interior and boundary layers to appear in the solution. To obtain appropriate point-wise accuracy, we have considered a central finite-difference approach in the space variable which is defined on a piecewise uniform Shishkin mesh and an implicit Euler scheme in the temporal variable defined on a uniform mesh. Some computational experiments have been performed, which confirm the theoretical findings.
查看更多>>摘要：? 2022 Elsevier Inc.Consider an insurer with d lines of business and the freedom to make risk-free and risky investments. The investment portfolio price process is described as a general càdlàg process. It is assumed that the claim sizes from different lines of business and their common inter-arrival times form a sequence of independent and identically distributed (i.i.d.) random pairs, each pair obeying a particular dependence structure. With this dependence structure, claim sizes from different lines of business are distributed according to the multivariate regular variation. This paper proposes conditions that can be satisfied by several important stochastic processes, including the Lévy process, Vasicek interest rate model, Cox-Ingersoll-Ross interest rate model, Heston model, and Stochastic volatility model. Under these conditions, the uniform asymptotic expansions of ruin probabilities are derived, which hold uniformly for the entire time horizon. Numerical examples are provided as a means of illustrating the main results.
查看更多>>摘要：? 2022 Elsevier Inc.This note investigates the stabilities for impulsive stochastic delayed Cohen-Grossberg neural networks driven by Lévy noise (ISDCGNNs-LN), including the input-to-state stability (ISS), integral input-to-state stability (iISS) and ?θ(t)-weight input-to-state stability (?θ(t)-weight ISS, θ>0). Utilizing the multiple Lyapunov-Krasovskii (L-K) functions, principle of comparison, constant variation method and average impulsive interval (AII) method, adequate ISS-type stability conditions of the ISDCGNNs-LN under stable impulse and unstable impulse are obtained. This shows that the stochastic systems are ISS in regard to a lower bound of the AII, provided that the continuous stochastic systems is ISS but has destabilizing impulse. Furthermore, the impulse can effectively stabilize the stochastic systems for a upper bound of the AII, provided that the continuous stochastic systems is not ISS. In addition, our results can also deal with the case of variable time delay. In the end, two examples are presented to reflect the rationality and correctness for the theoretical conclusions.
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