In this paper, we analyze the complex dynamics of a discrete-time, Leslie-type predator–prey system that exhibits a weak Allee effect where the prey population has a mate-finding Allee effect. This discrete mathematical model has been obtained by applying the forward Euler scheme to its continuous-time counterpart. First, stability and bifurcation analyses are performed to explore the stability of

We present a method for manipulating the Photonic Spin Hall Effect (PSHE) by examining the characteristics of an atomic ensemble with two levels connected to a high-quality cavity. Although the cavity is initially in a vacuum state with no external excitation, a substantial change can be made to the atomic ensemble’s probe response. A coherent effect analogous to electromagnetically induced transparency

Intermittent transitions, associated with critical dynamics and characterized by power-law distributions, are commonly observed during sleep. These critical behaviors are evident at the microscopic level through neuronal avalanches and at the macroscopic level through transitions between sleep stages. To clarify these empirical observations, models grounded in statistical physics have been proposed

Vortices as fundamental topological excitations are ubiquitous in nature and have attracted great interest in diverse contexts of science and engineering. We find a variety of novel topological defects in Rydberg-dressed Bose gas with spin-orbit coupling theoretically. A quantized vortex spontaneously breaks its azimuthal invariance, leading to the formation of discrete vortex around the supersolid

This paper presents the derivation of exact solutions to both space fractional-order and space–time fractional-order time-delayed diffusion equations, incorporating specific initial conditions. The exact solutions can be expressed as a series utilizing Fourier-Laplace transform methods in conjunction with the properties of delay fractional Mittag-Leffler functions. Our analysis reveals that when the

We theoretically study the azimuthal and radial vortex modulation via four-wave mixing (FWM) in superconducting artificial atoms. When both control fields carry orbital angular momentum (OAM), the intensity and phase distribution of the FWM field can be flexibly modulated by adjusting the azimuthal and radial indices of the two OAM modes. If only one control field is in a superposition of two OAM modes

In this paper, we investigate the geometry of the Jacobean tensor field generated by Hamiltonian flow in Hénon–Heiles potential. For this purpose, we have developed a new method for calculating the Jacobian tensor field based on the Caley transformation, particularly suited for studying 2D problems. To enhance its visualization, the Rotation-Diagonal-Rotation decomposition of the matrices was introduced

Variability is a key aspect of memristors that hinders their usage in massive commercial applications. This study investigates the cycle-to-cycle variability of resistive switching devices fabricated using three different dielectric configurations: two monolayer insulators (Al2O3 or HfO2) or a HfO2/Al2O3 bilayer. Thousands of resistive switching (RS) current-voltage (I-V) curves were measured under

This paper investigates complex stochastic resonance in a two-dimensional airfoil system under random perturbations. We examine a classical two-dimensional airfoil model with nonlinear stiffness, focusing on the dynamic transitions between fixed points (FP) and limit cycles (LC) in a bistable region. We investigates a stochastic resonance phenomenon characterized by periodic transitions between FP

This study investigates the emergence of antiphase fully synchronous states (AFSs) in small-size systems with 1-simplex and 2-simplex interactions. We focus on the influence of system size (N) on the existence of AFSs and reveal that the interplay between the second-harmonic and three-body coupling terms within the 2-simplex, in conjunction with N, significantly impacts the formation of AFSs. Our analysis

Globally coupled oscillator systems with inertia exhibit complex synchronization patterns, among which the emergence of a couple of secondary synchronized clusters (SCs) in addition to the primary cluster (PC) is especially distinctive. Although previous studies have predominantly focused on the collective properties of the PC, the dynamics of individual clusters and their inter-cluster interactions

For forecasting the spread of new goods and technology, the Bass diffusion model is an extremely important model. While this model fully considers the product life cycle, it lacks a comprehensive consideration of uncertain factors that influence products and customers’ demand. In many cases, describing these uncertain factors as stochastic processes in an approach may lead to certain issues. Therefore

A multi-scale model coupling within-host infection and between-host transmission with immune delay, infection age, multiple transmission routes and general incidence is developed based on the complexity of environmentally-driven infectious disease transmission. The model is composed of ordinary differential equations (ODEs), delay differential equations (DDEs), and a partial differential equation (PDE)

Multi-dimensional offset boosting is an important issue for chaos application, specifically it provides a new channel to obtain multiple unipolar signals for multi-carrier chaotic communication or multi-dimensional chaotic regulation. The conditions for two-dimensional offset boosting could be derived based on the feedback in chaotic map. After exhaustive computer-aided numerical simulation, a class

The nonlinear responses of primary resonance characteristics for the composite rotating blade are investigated in the presence of 1:2 internal resonance, where two primary resonance cases are considered, namely, the first mode and second mode being excited. The composite properties can be deduced via modified Halpin-Tsai micromechanics model and the rule of mixture. Lagrange formulation is employed

In nonlinear systems, the introduction of moiré lattice potentials significantly modifies the energy spectrum, giving rise to novel physical phenomena, such as the formation of flat bands and thus the rich local nonlinear structures. Furthermore, it is found that a deep moiré lattice leads to the degeneracy of Bloch eigenvalues. In this paper, we establish a fundamental relationship between the degeneracy

In recent years, the robustness of edge-coupled interdependent networks has been investigated and has attracted much attention from researchers in different fields. Currently, most research on edge-coupled interdependent networks focuses on two-layer systems with simpler RR or ER topologies. However, studies on multilayer edge-coupled interdependent Scale-Free networks are scarce. In this paper, we

As context-aware technology becoming more prevalent in a variety of applications, particularly in safety fields, it is increasingly important to evaluate the safety performance of context-aware systems (CASs). This paper addresses the safe control problem of general open-loop CASs by using the algebraic state-space representation, which is developed by the tool of the semi-tensor product (STP). Based

The result of the fractional derivative of a function which is the fractional differential equation, has been used to describe many physical phenomena such as composite fractional oscillation equation (CFOE), as it provides memory and hereditary properties of the CFOE. The solution of the CFOE is essential and is at the interest of every researcher. The numerical methods used in obtaining the solution

In a variety of application contexts, multi-component rogue waves have emerged as vital carriers of information about the physical mechanism. The purpose of this article is to study three-component annular rogue waves of the (2+1)-dimensional[(2+1)D] three-component nonlinear Schrödinger system, including annular single, double and triple rogue waves. Three-component dark–bright–dark annular rogue

The paper aims to improve the efficiency of modeling interactions between slender deformable bodies that resemble the shape of fibers. Interaction potentials are modeled as inverse-power laws with respect to the point-pair distance, and the complete body-body potential is obtained by pairwise summation (integration). To speed-up integration, we consider the analytical pre-integration of potentials

This paper focuses on the construction of nonlinear dynamic models, specifically targeting continuous chaotic systems. It introduces an innovative approach to integrating state variables and uncertain variables to construct continuous chaotic systems. Initially, a unified construction method is proposed, combining state variables with a determinable amplitude matrix. The feasibility of this method

This paper proposes a mathematical modeling of operation loop ratio (OLR) for assessing the importance of nodes within a combat network. Traditional models or indicators for evaluating node importance focus on the structural characteristics of a single node’s neighborhood, neglecting the supporting role of nodes in the overall performance of the network system during actual combat. Therefore, we propose

This paper is dedicated to the construction of integrable commuting flows starting from a fourth-order matrix spectral problem involving four fields, which is derived from a specialized matrix Lie algebra over the real domain. This work includes the development of an explicit bi-Hamiltonian formulation and a hereditary recursion structure, which confirms the hierarchy’s integrability in the Liouville

This study introduces a new stochastic microorganism flocculation model that takes into account saturated control and environmental noise, in which inhibitors are used as control variables. Due to the difficulty in deriving the optimal control through solving state equations and adjoint equations, this paper investigates a near-optimal control problem, aiming to effectively control the growth of harmful

The research here endeavors to delve into the trapezoid-type inequalities pertaining to multiplicative (k,s)-fractional integrals. To this end, we introduce a class of operators, called the multiplicative (k,s)-fractional integrals, and subsequently give an analysis of these newly minted operators, examining their characteristics including boundedness, continuity, commutative properties, semigroup

The feedback between strategy and environment is ubiquitous in nature and human society, which has been receiving increasing attention from researchers. Meanwhile, Q-learning allows players to explore the optimal strategy by interacting with the environment. In this paper, we introduce the Q-learning into the spatial public goods game with environmental feedbacks. The simulation results show that the

Insurance, a pivotal risk management tool in economic activities, protects participants in the public goods game from exploitation by defectors. In this study, we incorporate an insurance mechanism into spatial public goods games, empowering all participants to opt for insurance. By exploring phase transitions and spatial dynamics across various systems, we investigate the competition among multiple

Quantum reservoir computing (QRC) exploits the dynamical properties of quantum systems to perform machine learning tasks. We demonstrate that optimal performance in QRC can be achieved without relying on disordered systems. Systems with all-to-all topologies and random couplings are generally considered to minimize redundancies and enhance performance. In contrast, our work investigates the one-dimensional

In the current pursuit of extreme laser efficiency in fields such as optical communication, how can we achieve optimal transmission effects with minimal energy consumption? The angle has emerged as a crucial key in this endeavor. This paper aims to investigate the impact of inter-ring angles on the transmission efficiency of dual-ring Airyprime-Gaussian beam array (DAPGBA), specifically analyzing the

In the traffic road physical environment, there are many physical factors that affect vehicles speed, such as slopes, bends, and spiral roads. For vehicle safety on non-flat road, the speed restriction requirements are applied for road management. Especially in the mixed traffic involving connected autonomous vehicles (CAVs) and human-driven vehicles (HDVs), it is even more necessary to enhance vehicle

We reformulate the phenomenon of maximal entanglement conservation in Quantum Electrodynamics (QED) scattering processes, previously discussed in earlier works, using the tools of quantum maps and invariant sets. These sets are characterized as hypersurfaces within the six-dimensional parameter space. Furthermore, we speculate over a possible irreversible (ever-increasing) behavior of entanglement

In spatial public goods games (SPGG), the use of rewards serves as an effective strategy to enhance cooperation among group members. In this scenario, the rewarder incurs a cost to incentivize altruistic behavior. However, many individuals who are willing to cooperate are unwilling to bear the cost of incentives and thus become second-order free-riders. To address this issue, we propose a tax allocation

Axelrod’s model and its subsequent studies have become a valuable framework for fostering cooperation norms among self-interested agents. Within this framework, the concepts of “boldness” and “vengefulness” are specifically employed to characterize agents’ behaviors in terms of cooperation and punishment (including metapunishment). Describing behavior solely through the parameters B and V may be overly

In this paper, we present a general thermodynamically consistent hydrodynamic phase-field model for nonisothermal binary viscous fluids. This model incorporates cross-coupling effects among phase, velocity and temperature, while adhering to the generalized Onsager principle and conservation laws. We systematically explore its validity across the model parameter space and provide guidelines for determining

Optical diametric drive acceleration, also known as self-acceleration, has been predicted theoretically and verified experimentally in one-dimensional(1D) photonic lattices, which appears as two beams bending in the same direction. This phenomenon results from the interaction between two beams with positive and negative effective masses which are defined by energy band curvature. In contrast to 1D

This paper presents a novel approach for controlling the DLR-HIT II robotic hand by leveraging physics-informed neural networks (PINNs) for torque and position control. This method eliminates the need for additional control inputs or external controllers, achieving high precision and simplified dynamics, which is validated through extensive simulations that closely replicate experimental conditions

This paper presents a two-grid finite element method for solving semilinear fractional evolution equations on bounded convex domains. In contrast to existing studies that assume strong regularity for the exact solution, our approach rigorously addresses the limited smoothing properties of the fractional model. Through a combination of semigroup theory and energy estimates, we derive optimal error bounds

The problem of identifying mechanisms of abrupt changes in the dynamics of coupled stochastic systems is investigated. This problem is studied for a metapopulation consisting of two functionally coupled chaotic subsystems modeled by the Ricker map with Allee effect. For the initial deterministic model, a variety of dynamical modes with chaos-order transformations, different regimes of synchronization

Much effort has been paid to epidemic models built by ordinary differential equations (ODEs), partial differential equations (PDEs), or stochastic differential equations (SDEs) and received remarkable achievement. Different from these models, we establish and analyze a SIR epidemic model by using stochastic partial differential equations (SPDEs) in this paper, which incorporates the influence of inevitable

We study a general class of bivariate fractional integral operators, derived from bivariate analytic kernel functions by a double substitution of variables and a double convolution. We also study the associated bivariate fractional derivative operators, derived by combining partial derivatives with the aforementioned fractional integrals. These operators give rise to a theory of two-dimensional fractional

In this paper, we investigate the interconnection between players' strategies and the probability of effective punishment. We propose to integrate the environmental feedback and a punishment mechanism to construct a Prisoner's Dilemma game model within a regular network. Based on our analysis, we identify three unique system states: a single stable state where defection predominates and the probability

Discrete nonlinear Schrödinger equations (DNLSEs) are fundamental in describing wave dynamics in nonlinear lattices across various systems, including optics and cold atomic physics. With the advent of topological phases of matter, the DNLSEs that characterize nonlinear topological states and topological solitons in nonlinear topological systems have become increasingly complex. Newton’s method, which

We investigate the dynamics of quasi-one-dimensional Bose–Einstein condensates (BECs) with spin–orbit and Rabi couplings focusing on the role of nonlinear interactions in shaping the stability and dynamics of quantum phases like plane-wave and stripe-wave phases. Using the Bogoliubov–de-Gennes theory, we first analyze the stability of binary BECs with and without spin–orbit and Rabi couplings. Our

This paper investigates statics and dynamics of two-dimensional (2D) linear elastic lattices and their continuum approximations. Focus is on the mixed differential-difference equations proposed by Born and von Kármán in 1912 for cubic lattices with both central and non-central interactions, applied here to 2D lattices. The non-central interaction introduced by Born and von Kármán, classified as a shear

This paper proposes a novel neural network-based dynamic output feedback controller (NN-DOFC) for nonlinear systems subject to hybrid cyber-attacks. The nonlinear terms are modeled using Takagi–Sugeno fuzzy inference rules, and the NN-DOFC is introduced to ensure that the closed-loop system achieves asymptotic stability while satisfying the (X,Y,Z)-dissipative property. The conventional DOFC’s gains

The mathematical modeling of compressible flows in both rigid and elastic pipes is discussed here. Both single- and two-phase flow modeling are considered in the present paper. First, the derivation of the models through the integration of the 3-D equations over the radially deformable inner pipe cross-section is described. Then, the Coleman-Noll procedure is used in order to formulate constitutive/closure

We present an adaptation of a relatively simple topological argument to show the existence of many periodic orbits in an infinite dimensional dynamical system, provided that the system is close to a one-dimensional map in a certain sense. Namely, we prove a Sharkovskii-type theorem: if the system has a periodic orbit of basic period m, then it must have all periodic orbits of periods n⊳m, for n preceding