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Networks and Heterogeneous Media
Scopus
ISSN 1556-1801 · AIMS Press · 828 articles in the index
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Journal Article
Legendre spectral-Monte Carlo method and its error analysis for nonlinear stochastic Itô–Volterra integral equation
Nonlinear stochastic Itô–Volterra integral equations (NSIVIEs) represent systems whose current state is influenced by random fluctuations and is dependent on previous information. These equations appear in many real-world scenarios, including engineering systems, biological processes, financial…
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Journal Article
An enhanced crossover strategy for the artificial lemming algorithm for engineering design optimization
To address the limitations of the artificial lemming algorithm (ALA) in convergence accuracy and premature convergence, this paper proposes an enhanced variant, the cross-strategy-integrated artificial lemming algorithm (CALA). Specifically, the CALA integrates a linear inertia weight strategy to…
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Journal Article
Weighted Morrey space boundedness for Hörmander-type singular integrals
We investigate the boundedness properties of singular integral operators characterized by $ L^{r} $-Hörmander kernel conditions (for $ 1 < r < \infty $) within the framework of weighted Morrey spaces. Additionally, the analysis is extended to commutators generated by these operators and functions…
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Journal Article
Stability and Hopf bifurcation analysis of Caputo time-fractional delayed reaction-diffusion models for sterile insect technology
Based on the theory of fractional differential equations, this paper studied a single-species contraception model with feedback control terms. By comprehensively applying the Mittag-Leffler function construction method, Laplace transform, and stability criteria for fractional-order systems, the…
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Journal Article
Dual-Uncertainty modeling in financial time-series via VMD-LSTM with concrete dropout and VMD-WGAN
Financial time-series forecasting requires not only accurate point predictions but also a principled characterization of the uncertainty around future outcomes. We proposed a unified dual-path framework that modeled both forms using a shared variational mode decomposition (VMD) backbone. VMD…
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Journal Article
Quantized $ \mathcal{H}_\infty $ synchronization for Hopfield networks subject to time-variable delay
This paper is dedicated to the study of $ \mathcal{H}_\infty $ synchronization for Hopfield networks (HNs) with time-variable delay via quantized control. The delay function is assumed to be continuous and bounded, yet not necessarily differentiable. A delay-dependent sufficient condition is…
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Journal Article
A non-conservative, non-local approximation of the Burgers equation
The analysis of non-local regularisations of scalar conservation laws is an active research program. Applications of such equations are found in modelling physical phenomena, such as traffic flow. In this paper, we propose an inviscid, non-local regularisation in a non-divergence form. The salient…
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Journal Article
On the number of limit cycles of a class of near-Hamiltonian systems near a degenerate center
In this paper, we focused on studying the number of limit cycles of a class of near-Hamiltonian systems, whose unperturbed system possesses a degenerate center. Using the first order Melnikov function, we obtained the lower bound of the maximum number of limit cycles in Poincaré bifurcation under…
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Journal Article
Numerical approximation of fourth-order fractional diffusion-wave systems using finite difference and discontinuous Galerkin method
This study develops a finite difference/local discontinuous Galerkin (LDG) framework for solving a fourth-order fractional diffusion-wave equation. The temporal fractional operator is approximated through a finite difference approach, achieving a truncation accuracy of $ O((\Delta t)^{3-\alpha}) $…
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Journal Article
An effective numerical method for simulating a class of fractional-order chaotic system
This paper investigates the chaotic dynamics and control of fractional-order chaotic systems. A high-precision numerical method based on the Grünwald–Letnikov definition is developed to explore the system's dynamics. We also design linear feedback and adaptive control strategies to achieve chaotic…
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Journal Article
Exploring dynamics and pattern formation of a fractional-order three-variable Oregonator model
In this paper, we investigated the nonlinear dynamics and pattern formation of a fractional-order three-variable Oregonator model. We first performed a linear stability analysis of the model without diffusion, deriving equilibrium points and Jacobian eigenvalues, and verified Matignon's stability…
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Journal Article
Weighted implicit-explicit discontinuous Galerkin methods for two-dimensional Ginzburg–Landau equations on general meshes
In this paper, a second-order linearized discontinuous Galerkin method on general meshes, which treats the backward differentiation formula of order two (BDF2) and Crank–Nicolson schemes as special cases, is proposed for solving the two-dimensional Ginzburg–Landau equations with cubic nonlinearity…
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Journal Article
Dynamics of the discrete-time man-environment-man epidemic model with a free boundary
In this paper, we investigate the discrete-time man-environment-man epidemic model with a free boundary, which can be viewed as a time-discrete version of the free boundary model studied by Ahn, Beak, and Lin. First, applying the properties of the principal eigenvalue of the corresponding…
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Journal Article
Supercloseness of the NIPG method on Bakhvalov-type meshes for a system of singularly perturbed reaction-diffusion equations
In this paper, a higher order nonsymmetric interior penalty Galerkin (NIPG) method on a Bakhvalov mesh is developed for a weakly coupled system of singularly perturbed reaction-diffusion equations. At first, by selecting special penalty parameters at different mesh points, the supercloseness of the…
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Journal Article
Kinetic modeling approach for a heterogeneous neuronal network activity using adjacency matrices
The heterogeneity of neuronal networks plays a crucial role in shaping emergent dynamics. In this work, we introduced a kinetic modeling approach to describe the activity of heterogeneous neuronal networks through transition probabilities and adjacency matrices. The model explicitly accounts for…
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Journal Article
Prescribed-time stabilization for nonlinear systems via hybrid continuous and dynamic event-triggered impulsive control
Here, by integrating continuous control and dynamic event-triggered impulsive control (DETIC) based on a piecewise function ratio framework, a hybrid control strategy is developed to solve prescribed-time stabilization (PTS) for nonlinear systems. Different from the traditional methods, the…
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Journal Article
Numerical computation of generalized Wasserstein distances with applications to traffic model analysis
Generalized Wasserstein distances allow us to quantitatively compare two continuous or atomic mass distributions with equal or different total masses. In this paper, we propose four numerical methods for the approximation of three different generalized Wasserstein distances introduced in the past…
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Journal Article
Convergence analysis of a second-order finite difference scheme on Shishkin-type meshes for a singularly perturbed Volterra integro-differential equation
In this paper, a novel second-order numerical method on a Shishkin mesh is constructed to solve a singularly perturbed Volterra integro-differential equation. The proposed numerical scheme employs a second-order backward differentiation formula (BDF2) for discretizing the first-order derivative…
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Journal Article
Saddlepoint approximation for the bivariate two-sample tests under the random allocation design
This article addresses the challenge of accurately estimating p-values in bivariate two-sample tests under random allocation designs, a common setting in clinical and reliability studies. Existing normal approximations often perform poorly in small samples and in the distribution tails, leading to…
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Journal Article
Optimal control of queuing systems governed by integro-differential equations
In this research, we advanced the optimal control theory for queuing systems that are characterized by integro-differential equations. Our primary goal was to identify an optimal service rate that minimizes a performance criterion, which is a composite of the system state at the final time and the…