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This study examines significant applications across various domains, including microfluidics, biomedical engineering, and energy systems, focusing on the advancement of lab‐on‐a‐chip technologies, electrokinetic pumps, and micro‐scale filtration systems. A detailed investigation is conducted to explore the combined influence of peristaltic transport, double‐diffusive convection, electroosmosis, magnetohydrodynamics

Achieving effective vibration isolation across a broad frequency range while simultaneously harvesting energy from vibrations remains a key challenge in engineering systems. This study examines the nonlinear dynamics and vibration isolation performance of an oblique-type spring quasi-zero stiffness (QZS) isolator integrated with a piezoelectric energy harvester. The coupled system is modeled as a strongly

The evolutionary dynamics of cooperation in threshold-dependent public goods provision remains poorly understood in systems with higher-order interactions. To address the gap, we introduce an evolutionary hypergraph-based threshold public goods game, where collective contributions within a group (hyperedge) must exceed a threshold value ? to generate shared benefits. Our results reveal that, in uniform

The chaos is a complex phenomenon that appears random but actually possesses inherent patterns. The study of chaos is significant for understanding many complex phenomena in nature. This paper aims to explore the threshold curves of the chaos phenomenon by analyzing the homoclinic orbits and global dynamics of the doubly-excited Duffing–van der Pol system using the homotopy analysis method and Melnikov

With the promotion of policies and technological progress, accelerate the advancement of Internet of Vehicles (IOVs) and refine it considerably, and then the real-time communication of vehicle-vehicle, vehicle-infrastructure and vehicle cloud will be realized, which will provide more abundant data for connected vehicles (CVs); however, the large-scale popularization of the vehicle was a drawn-out procedure

To enhance the robustness of SD oscillator system, an electromagnet with state feedback control is introduced above the oscillator, considering the nonlinear characteristics of the electromagnetic force. Initially, the system's steady-state amplitude-frequency response, phase-frequency response, and backbone curve are determined using the averaging method. These results are compared with the traditional

We propose a collective motion model incorporating selective interactions through a Motion Salience Threshold (MST) mechanism, where particles dynamically switch between an active state responding to significant motion cues and an inactive state aligning with local average orientation. This selective interaction mechanism enables particles to filter out minor fluctuations while maintaining sensitivity

Turbulence and oscillating amplitude of boundary layers and nonlinear radiative heat and concentration motion of transient Williamson nanomaterial model alongside inclined solar surface with entropy optimization, magnetic oscillation, dynamic solar energy, and thermo diffusion is the novelty of this work. The objective of this problem is to scrutinize the speed streamlines, isothermal lines, energy/temperature

The experimental assessment of networks within a complex system requires the inference of links. A common way to detect a link relies on the assumption that time series recorded out of two nodes contain sufficient shared information so as to detect a correlation, using either linear measures or more sensitive information-theoretical tools. While this assumption is theoretically granted for any system

Continuous firing patterns in biological neurons result from time-varying electromagnetic field accompanied by energy exchange between magnetic field and electric field in the cell, which the intracellular ions are diffused and membrane channels are open for ions propagation across the outer and inner cell membranes. Incorporation of memristive terms of the neuron models can describe the effect of

Optimizing energy transport and enhancing its efficiency in electro-thermal systems is of significant importance for advanced thermal management and energy sustainability. The present study focuses on the analysis of time-dependent electrically conducting disks enduring convective heat and comprising a permeable medium with Alumina and Graphene oxide immersed in water. The thermal distribution is studied

We consider a nonlinear oscillator with state-dependent time-delay that displays a countably infinite number of nested limit cycle attractors, i.e. megastability. In the low-memory regime, the equation reduces to a self-excited nonlinear oscillator and we use averaging methods to analytically show quasilinear increasing amplitude of the megastable spectrum of quantized quasicircular orbits. We further

In this work, we investigate a three-species Lotka–Volterra model incorporating omnivorous interactions, characterized by cross-trophic feeding behavior, and propose a novel predator strategy in which prudent predators avoid attacking aggressive individuals. Through rigorous mathematical analysis, we conduct a comprehensive examination of equilibrium existence and stability conditions, systematically

Here, we propose a unified approach to reproduce the Mandelbrot set, some inner structures of the period bulbs, and the complement of the Mandelbrot set. The special feature of the method is not only that all these structures are visualized with a single algorithm but also that it distinguishes mechanism that act on different time scales and, furthermore, its exceptional sensitivity, which approaches

In this paper, the three-coupled nonlinear Schr?dinger equation, representing the complex optical pulse in three mode optical fibers, is discussed by the Hirota method. The stable transmissions of nondegenerate three-hump solitons are constructed. The evolutions of nondegenerate three-hump solitons to nondegenerate double-hump solitons and degenerate single-hump solitons are also discovered. The soliton

Critical points separate distinct dynamical regimes of complex systems, often delimiting functional or macroscopic phases in which the system operates. However, the long-term prediction of critical regimes and behaviors is challenging given the narrow set of parameters from which they emerge. Here, we propose a framework to learn the rules that govern the dynamic processes of a system. The learned

A crane system has a variety of applications in industry and for research purposes. However, this system is underactuated and is always affected by disturbances, which compromises the controller design stage. Then, this work develops a new control scheme to control two-dimensional (2D) perturbed overhead cranes. The new proposal separates the controller into two parts. The first controller component

In this paper, we present an arbitrarily high-order numerical scheme for the two-component Camassa–Holm system, ensuring the preservation of three invariants: energy and two Casimir functions. The spatial discretization is achieved using Fourier–Galerkin methods, resulting in a semi-discrete system which retains a Hamiltonian structure and approximates the invariants of the original continuous system

In ecological and ecosystem studies, spatiotemporal distribution patterns are identified as crucial factors in maintaining species diversity. Specifically, spiral waves, which are a typical spatiotemporal pattern, are prevalent across various ecosystems, including both continuous and discrete-time systems. In continuous-time systems, spiral waves are commonly associated with Hopf bifurcations. This

To address the issue of information security, we introduce a novel car-following model with electronic throttle functionalities that integrates continuous memory to mitigate cyber-attacks within a context of connected vehicles. This model is analyzed in two scenarios including suddenly stopping once and four times of the leading car at following two cases: Case 1, where connected vehicles operate normally

Two-dimensional multi-term time-fractional diffusion-wave equations (TFDWEs) have numerous applications in fields such as material science, complex media, thermodynamics, heat conduction, quantum systems, finance, and economics. This study focuses on solving a specific type of 2D TFDWE by developing a pseudo-operational collocation scheme that utilizes three-variable Jacobi polynomials over the domain

Recent developments in generative modeling have utilized score-based methods coupled with stochastic differential equations to sample from complex probability distributions. However, these and other performant sampling methods generally require gradients of the target probability distribution, which can be unavailable or computationally prohibitive in many scientific and engineering applications. Here

The research of bursting oscillations in neuronal models not only enriches the study of nonlinear dynamics, but also deepens the understanding of the working mechanism of the brain. A coupled FitzHugh-Nagumo (FHN) neuron model can be simulated by connecting two resistor-inductor-capacitor circuits via a resistor. Taking into account the external excitation as a slow variable, the FHN neuron model can

Nowadays, increasing pollution problems in major basins in China are becoming serious due to the acceleration of urbanization, and transboundary pollution problems are particularly deteriorating. The pollutants generated by production in the upstream area enter the midstream area with water flow and eventually reach the downstream area, causing adverse effects on the local ecological environment and

In this paper, we explore a class of time-dependent mixed quasi-variational-hemivariational inequality problems (TMQVHVI), which are characterized by the dependence of their constraint set on the solutions. We prove a solvability result for TMQVHVI by using a static mixed quasi-variational–hemivariational inequality and a measurable selection lemma. And, moreover, the boundedness and closedness of

We investigate the dynamics of maps of the real line whose behavior on an invariant interval is close to a rational rotation on the circle. We concentrate on a specific two-parameter family, describing the dynamics arising from models in game theory, mathematical biology and machine learning. If one parameter is a rational number, k/n, with k,n coprime, and the second one is large enough, we prove

The Local Randomized Neural Networks with Discontinuous Galerkin (LRNN-DG) methods, introduced in Sun et al. (2024), were originally designed for solving linear partial differential equations. In this paper, we extend the LRNN-DG methods to solve nonlinear PDEs, specifically the Korteweg–de Vries (KdV) equation and the Burgers equation, utilizing a space–time approach. Additionally, we introduce adaptive

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Anti-preferential attachment is a social network formation mechanism where nodes with a lower degree have more chances of acquiring new connections. Recent findings indicate interesting conditions under which anti-preferential attachment appears: it has been documented that pairs of online users with one or more friends in common are more likely to become friends if they have low degrees. Among pairs

In this study, we consider a stress-strength model of the k-out-of-n system which has n statistically independent and different strength components. The components of the system are exposed to a common random stress, and the component strengths and the common stress follow different exponentiated gamma (EG) distributions. The inverse moment estimator and the maximum likelihood estimator of the reliability

We investigate the radial injection of a shear-thinning fluid, initially occupying a disk of a given radius, into the narrow gap between two parallel plates, displacing a viscous Newtonian fluid. In the Newtonian analogue, the Saffman-Taylor fingering instability occurs when a more viscous fluid is displaced by a less viscous one. Further complications arise when the displacing fluid is shear-thinning

This paper introduces a novel varying-coefficient autoregressive model that includes an explanatory variable and a non-stationary state equation to analyze and predict complex time series data. The model incorporates a function that evolves over time, which provides a sophisticated understanding for analyzing data with nonlinear and non-stationary characteristics. Some key statistical properties of

This paper deals with an intergenerational utility maximization problem for consuming a naturally exhaustible resource. In this context, we are at odds with the unfair standard procedure of applying a time-dependent factor for discounting the utility and introducing a suitable function for penalizing overconsumption. A finite-time horizon dynamic stochastic optimization problem is presented to achieve

Evaluating the propagation influence of nodes is crucial for understanding the survival and robustness of networks. In recent years, numerous methods have been widely applied to identify high-influence nodes, such as degree centrality and K-shell decomposition, which are based on single network features. However, these methods often fail to fully capture the propagation potential of nodes. To improve

We study the existence of dark gap quantum droplet (DGQD) families in the nonlinear Schr?dinger equation with linear lattices, including both individual DGQDs and their clusters. Two types of linear lattices are studied in this work, monochromatic and bichromatic. The backgrounds of these families in bichromatic lattices differ from those in monochromatic lattices, being composed of two lattices instead

One-step generation of W-state entangled three-photons based on spontaneous six-wave mixing (SSWM) has been shown to have significant advantages over cascaded spontaneous parametric down conversion (SPDC) methods and cascaded spontaneous four-wave mixing (SFWM) methods. On this basis, this paper provides a theoretical insight into the optical response in non-Hermitian SSWM systems under linear and

This paper is devoted to studying the following spatially periodic reaction–diffusion equation with bistable nonlinearity: ?tu???(A(x)?u)=f(x,u),t∈R,x∈RN.We investigate the effect of spatial heterogeneity on the propagation phenomenon of parabolic equations in RN. As a special entire solution, traveling waves play a significant role in studying the dynamic behavior of reaction–diffusion equations.

The stiffness of a shell is conclusively influenced by the distribution of its material. To obtain the optimal material distribution of 3D spatial shells at a reasonable computational cost, this paper proposes a layer-by-layer optimization strategy with controllable deformation. In this strategy, the 3D spatial shell is divided into finite layers in the thickness dimension, and the deformations of

We discuss the synchronization control problem for a network of Euler–Bernoulli beam equations with freedom at both ends and time-varying disturbances at the boundary. First, we present the aim of the control of this paper. Next, the reference signal is provided, allowing us to transform the control objective into a form that includes the virtual reference signal. Then, by the method of active disturbance

In this study, we introduce two recent algorithms designed to solve the split variational inclusion problem in Banach spaces by using two inertial extrapolations and self-adaptive step size technique. Theoretical analysis demonstrates that the inertial Mann-type self-adaptive algorithm (IMSA) and the inertial Halpern-type self-adaptive algorithm (IHSA) generate strong convergence under the specified