Dynamic Behavior Research Articles

GLOBAL STABILITY OF AN SEIS EPIDEMIC MODEL WITH BEDDINGTON-DEANGELIS INFECTION RATE

In this paper, the global dynamic behaviors of an SEIS epidemic model with Beddington-DeAngelis infection rate are investigated. This model takes into account constant recruitment, death from the disease, and the phenomenon of latency. Under some hypotheses, it is shown that the global dynamics is determined by the basic reproduction number $R_0$. If $R_0$ is less than unity, the disease-free equilibrium is both locally and globally stable and the disease dies out. If $R_0$ is greater than unity, sufficient conditions for the global stability of the endemic equilibrium are obtained by the geometric approach of Li and Muldowney. Some numerical simulations are also presented to confirm the analytical results.

Dynamic mechanical response of TaMoNbZrTi refractory high entropy alloy via multi-wire arc additive manufacturing

ABSTRACT Here, the TaMoNbZrTi refractory high entropy alloy (RHEA) is fabricated by multi-wire arc additive manufacturing (MWAAM), and the dynamic mechanical behaviour is analysed. A pre-alloyed droplet transfer mode is proposed to facilitate decent metallurgical reactions of different wire feedstocks, with the assistance of hot-wire and pulsed arc processing. The RHEA exhibits dendritic microstructures and consists of two Body-Centered-Cubic (BCC) phases. Dynamic compression testing suggests that as the strain rate increases from 920 to 4100 s−1, the yield strength of the RHEA is boosted by ∼158%, and the fracture strain increases by ∼72%. More dislocations appear at the Zr-Ti-rich interdendritic region with 4.0 × 1014 /m2 geometrically necessary dislocations (GND) density, compared with the dendrite with 2.1 × 1014 /m2 GND density, and they accumulate around the Ta-Mo-Nb-rich cellular particles. Our work provides an efficient pathway for the one-step additive manufacturing of RHEAs and makes a pioneering exploration of their microstructures and dynamic mechanical behaviour.

Exploration of the effect of fractional elements in nonlinear transmission lines

Purpose The purpose of this paper is to explore how fractional derivatives affect the transient and steady-state behaviour of nonlinear transmission lines. This problem is of significance for high-frequency design of systems such as high-speed sampling systems and radar systems. Design/methodology/approach This paper shall consider the transient and steady-state responses of nonlinear transmission lines when fractional derivatives are considered. A lumped-parameter model is considered and the product-integration implicit trapezoidal rule shall be used for simulations. Findings The important observation is that small deviations of the order of the derivative from an integer order can have a significant effect on the transient and steady-state behaviour. This includes a change in the speed of the wave on the transmission line and on its damping. Originality/value The work is novel as it uses a lumped-parameter model with nonlinear capacitors and explores the effect on the dynamical behaviour when fractional derivatives are present. This is in contrast to the typical approach of using a partial differential equation derived under certain assumptions such as the nature of the nonlinear capacitor.

Bifurcations and exact solutions of the complex Ginzburg–Landau equation with Kudryashov's law

In this paper, we investigate the complex Ginzburg–Landau equation with Kudryashov's law using the method of dynamical systems. By using travelling-wave transformation, the model can be converted into a singular integrable travelling-wave system. Then we discuss the dynamical behaviour of the associated regular system and we obtain bifurcations of the phase portraits of the travelling-wave system under different parameter conditions. Finally, under different parameter conditions, we obtain the exact periodic solutions, homoclinic and peakon solutions.

Recent Advances in the Performance and Mechanisms of High-Entropy Alloys Under Low- and High-Temperature Conditions

High-entropy alloys, since their development, have demonstrated great potential for applications in extreme temperatures. This article reviews recent progress in their mechanical performance, microstructural evolution, and deformation mechanisms at low and high temperatures. Under low-temperature conditions, the focus is on alloys with face-centered cubic, body-centered cubic, and multi-phase structures. Special attention is given to their strength, toughness, strain-hardening capacity, and plastic-toughening mechanisms in cold environments. The key roles of lattice distortion, nanoscale twin formation, and deformation-induced martensitic transformation in enhancing low-temperature performance are highlighted. Dynamic mechanical behavior, microstructural evolution, and deformation characteristics at various strain rates under cold conditions are also summarized. Research progress on transition metal-based and refractory high-entropy alloys is reviewed for high-temperature environments, emphasizing their thermal stability, oxidation resistance, and frictional properties. The discussion reveals the importance of precipitation strengthening and multi-phase microstructure design in improving high-temperature strength and elasticity. Advanced fabrication methods, including additive manufacturing and high-pressure torsion, are examined to optimize microstructures and improve service performance. Finally, this review suggests that future research should focus on understanding low-temperature toughening mechanisms and enhancing high-temperature creep resistance. Further work on cost-effective alloy design, dynamic mechanical behavior exploration, and innovative fabrication methods will be essential. These efforts will help meet engineering demands in extreme environments.

MicroVasculoid‐Chip: A 3D Self‐Assembled Human Microcirculation‐on‐a‐Chip Model Reveals Enhanced Lymphangiogenic Lung Cancer‐Induced Vessel Remodeling and Invasion

AbstractThe microvasculature within the tumor microenvironment is crucial for the invasion and dissemination of cancer cells throughout the body. Given its importance and dynamic behavior, several microfluidic models have been developed to study microvascular infiltration and its interaction with cancer cells. However, most of these models primarily focus on blood vessels and use microfluidic channels coated with endothelial cells, which fail to replicate near‐physiological conditions. To address this limitation, the MicroVasculoid‐chip is introduced, a novel human microcirculation‐on‐a‐chip model that features self‐organized 3D blood and lymphatic microvasculature alongside tumor spheroids. This innovative platform enables the exploration of interactions between multi‐cellular tumors and both microvascular networks. Using lung cancer as a case study, how tumor‐released mediators influence vessel morphology is investigated in relation to tumor invasion capacity, identifying molecular factors potentially associated with microvascular remodeling. Overall, the MicroVasculoid‐chip provides a robust tool for investigating and modeling critical events of cancer neo‐vascularization, for deciphering fundamental mechanisms of cancer cell invasion into the microvasculature, and for future drug screening applications.

Accurate deep learning based method for real-time directly modulated laser modeling

Rate equations and numerical simulations relying on complex mathematical and physical principles are typically used to model directly modulated lasers (DMLs) but have difficulty simulating dynamic DML behavior in real-time under varying conditions due to their high complexity. Here, we introduce a data-driven deep learning method to model DMLs, aiming to achieve high accuracy with reduced computational complexity. This approach employs bidirectional long short-term memory (BiLSTM) enhanced by advanced feature recalibration and nonlinear fitting techniques. The result is compared with LSTM, standard BiLSTM, and recurrent neural network (RNN) architectures. The proposed model obtains the best results for the evaluated metrics. The satisfactory output waveforms and acceptable spectra indicate that the proposed model offers an accurate and real-time method to model DMLs.

A Study of the Doppler Effect in the Analysis of Black Hole Images

Black holes, one of the most mysterious objects in the universe, have long captured the attention of the scientific community due to their extreme gravity and intricate physics. In theory, a black hole is formed when a massive star or object collapses at the end of its life cycle. When a star exhausts its core energy and is no longer acted upon by external forces, it begins to collapse inward. This process continues until the star reaches a critical density, at which point its gravity becomes so strong that not even light can escape, forming a black hole. Black holes exert a profound influence on the universe, continuously absorbing matter in their vicinity, including gas, dust, and other celestial objects. Focusing on the core physical properties and related phenomena of black holes, this paper explores the profound impact of black holes on existing physical theories. By analyzing the motion of matter and energy release mechanism under the gravitational field of black holes, it reveals the complex dynamic behavior of black holes under extreme conditions. In addition, it emphasizes the existence of singularities and their challenges to physics theories, especially the limitations of quantum gravity theory. The study of the Doppler effect and the relativistic beam effect provides further evidence of the high-speed motion of the matter around a black hole and the changes in its radiation properties. These in-depth discussions provide new perspectives for understanding the quantum properties of black holes and their importance in astronomy.

Investigating nonlinear dynamic properties of an inertial sensor with rotational velocity-dependent rigidity

This study investigates the nonlinear dynamics of a system with frequency-dependent stiffness using a MEMS-based capacitive inertial sensor as a case study. The sensor is positioned directly on a rotating component of a machine and consists of a microbeam clamped at both ends by fixed supports with a fixed central proof mass. The nonlinear behavior is determined by electrostatic forces, axial and bending motion coupling, and frequency-dependent stiffness. The numerical Galerkin approach is employed for discretization of the coupled differential equations in spatial coordinates. To obtain the sensor response as a function of frequency, a continuation arc-length method based on weak formulation energy balance method is used. This approach uses a physical gradient descent learning based method to obtain unknown coefficients of the considered response. The presented method computes the periodic steady-state solution of the design by considering different frequency contents within the response, including different harmonics of the response expansion. However, the primary and secondary resonances at various harmonic frequencies within the response can be predicted. In this article, the dynamic behavior of the design is investigated by testing different levels of shaft acceleration and different bias voltages. The purpose of the evaluation is to determine the frequency-dependent stiffness of the accelerometer for different levels of shaft speed, taking into account various sensor geometric parameters. The analysis demonstrates the behavior of the sensors under different conditions, particularly highlighting the nonlinearity of the sensor, which causes primary and secondary resonances in the first, second, and third harmonic responses of the accelerometer, especially at higher bias voltages. Fast Fourier analyses indicated that the transversal vibration amplitude of the structure in the second and third harmonies are so considerable that cannot be neglected. The mathematical method used in this study can be applied by researchers and engineers in the design of such sensors to effectively create these devices.

Inter-event time power laws in heterogeneous systems

Abstract We investigate the dynamic behavior of spin reversal events in the dilute Ising model,
focusing on the influence of static disorder introduced by pinned spins. Our Monte Carlo simulations
reveal that in a homogeneous, defect-free system, the inter-event time (IET) between local
spin flips follows an exponential distribution, characteristic of Poissonian processes. However, in
heterogeneous systems where defects are present, we observe a significant departure from this
behavior. At high temperatures, the IET exhibits a power-law distribution resulting from the interplay
of spins located in varying potential environments, where defect density influences reversal
probabilities. At low temperatures, all site classes converge to a unique power-law distribution, regardless
of their potential, leading to distinct critical exponents for the high- and low-temperature
regimes. This transition from exponential to power-law behavior underscores the critical response
features of magnetic systems with defects, suggesting analogies to glassy dynamics. Our findings
highlight the complex mechanisms governing spin dynamics in disordered systems, with implications
for understanding the universal aspects of relaxation in glassy materials.

Defect related vortex dynamics behaviors in ‘1144’-type iron-based superconductors

Abstract We have synthesized ‘1144’- type (Ca1–x Pr x KFe4As4 and CaKFe4As4) and ‘122’-type (Ba0.6K0.4Fe2As2 and Ba0.6Rb0.4Fe2As2) iron-based superconductors. Based on these crystals, we have investigated the vortex dynamics of the ‘1144’- and ‘122’-type iron-based superconductors. The results indicate that the novel flux dynamics behaviors of the ‘1144’-type iron-based superconductors are closely related to their defect structures. First, the intergrowths in ‘1144’-type superconductors can function as columnar defects under an applied magnetic field H∥ab-plane, which results in a dip structure in the magnetization hysteresis loops (MHLs) near zero field due to the self-field effect. Second, the intergrowths, as strong pinning sites, provide a large pulling force on the flux lines and cause a small magnetization peak at temperatures below 10 K under magnetic fields from about 3–7 T in MHLs for the ‘1144’-type superconductors. Third, there may be vortex entanglement due to the presence of strong pinning centers, which impedes the elastic-to-plastic motion of vortices (E–P phase transition) resulting in a weak second magnetization peak (SMP) effect in the bulk ‘1144’-type superconductors. Fourth, the intergrowths introduce disorder into the superconductors and accelerate the magnetic 3D-to-2D transition, which causes the thickness-dependent J c and SMP effects due to the rigidity of flux lines with decreasing sample thickness. The current results are significant for our understanding of the relationship between the flux pinning behaviors and the defect structures for a superconductor.

Investigating wave solutions in coupled nonlinear Schrödinger equation: insights into bifurcation, chaos, and sensitivity

In this research, a systematic approach is employed to derive novel wave solutions for the coupled nonlinear Schrödinger equation. The transformation of the coupled partial differential equation into ordinary differential equation is achieved by utilizing a complex wave variable. Exponential function combinations are applied to construct the wave solutions. The accuracy of the derived solitons is validated through symbolic computations performed in Wolfram Mathematica, accompanied by graphical visualizations of the proposed solutions. The model is converted into a dynamical system, enabling qualitative and sensitivity analysis. Additionally, introducing perturbed terms is examined, revealing chaotic patterns in the system. The impact of variations in amplitude and frequency parameters on the system’s dynamical behaviour is thoroughly investigated. The findings underscore the efficiency and reliability of the applied techniques, demonstrating their applicability to a wide range of complex nonlinear systems.

Chaos, Fractals and Bifurcation in Real Dynamics of Two-Parameter Family Associated to Logarithmic Functions

The purpose of this article is to provide bifurcation diagrams and observe chaotic behaviour in the real dynamics of two-parameter family of function \(\Phi(x)=x+(1-\lambda x)\ln(ax): x>0, \lambda>0, a>0\). We consider here parameter a is a positive and continuous real parameter while λ is positive but a discrete real parameter. The dynamical properties of this nonlinear system family analyze numerically as well as graphically by using fixed point iterative method. Bifurcation diagrams for the real dynamics of the function are plotted by varying the values of the parameter which are fractals in nature. Also, we show that chaos exists in the dynamics of the function by looking at period-doubling in the bifurcation diagram. Further, chaotic behaviour studies by simulation of the positive Lyapunov exponents which observe by varying the parameters similar to the bifurcation diagrams.

Dynamic Compressive Behavior of a Carbonfiber- Reinforced Composite at Different Temperatures and Strain Rates

Dynamic Compressive Behavior of a Carbonfiber- Reinforced Composite at Different Temperatures and Strain Rates

Many-Objective Truss Structural Optimization Considering Dynamic and Stability Behaviors

The most commonly used objective function in structural optimization is weight minimization. Nodal displacements, compliance, the first natural frequency of vibration, the critical load factor concerning global stability, and others can also be considered additional objective functions. This paper aims to propose seven innovative many-objective structural optimization problems (MOSOPs) applied to 25-, 56-, 72-, 120-, and 582-bar trusses, not yet presented in the literature, in which the main objectives, in addition to the structure’s weight, refer to the structures’ vibrational and stability aspects. These characteristics are essential in designing structural models, such as the natural frequencies of vibration and load factors concerning global stability. Such new MOSOPs have more than three objective functions and are called many-objective structural optimization problems. The chosen objective functions refer to the structure’s weight, the natural frequencies of vibration, the difference between some of the natural frequencies of vibration, the critical load factor concerning the structure’s global stability, and the difference between some of its load factors. The sizing design variables are the cross-sectional areas of the bars (continuous or discrete). The methodology involves the finite element method (FEM) to obtain the objective functions and constraints and multi-objective evolutionary algorithms (MOEAs) based on differential evolution to solve the MOSOPs analyzed in this study. In addition, multi-criteria decision-making (MCDM) is adopted to extract the solutions from the Pareto fronts according to the artificial decision-maker’s (DM) preference scenarios, and the complete data for each chosen solution are provided. For the MOSOP with seven objective functions, it is possible to observe variations in the final weights of the optimum designs, considering the hypothetic scenarios, of 21.09% (25-bar truss), 289.73% (56-bar truss), 70.46% (72-bar truss), 45.35% (120-bar truss), and 74.92% (582-bar truss).

Static and Dynamic Mechanical Behavior of Lattice Structures of Shape Memory Alloys

Static and Dynamic Mechanical Behavior of Lattice Structures of Shape Memory Alloys

Characterization of the Dynamic Behavior of a Stirred Liquid–Liquid System for Process Control

AbstractThe dynamic behavior of a toluene/NaOH solution system was studied in a batch stirred tank. Characterization by step response experiments showed that the drop size response to stirrer speed steps behaves as a first‐order system, whereas the stirrer speed responds as a second‐order system. The respective time constants differed by at least one order of magnitude, suggesting effective control of the drop size is feasible by adjusting the stirrer speed. Based on experimental data, simple, linear system models were derived for the mean drop diameter and the interfacial area using the stirrer speed as input variable. Validation experiments showed good model qualities of about 70 % and the design of test trajectories proved the model's usability in an open‐loop control.

1:4 resonance, Arnold tongues and Marotto's chaos of a discrete reduced Lorenz system

In this paper, firstly, asymptotically embedding the fourth iterate of the normal form of a discrete reduced Lorenz system into a flow, we present rigorously the bifurcation sequence as the parameter varies around the 1:4 strong resonance point, from which an Arnold tongue corresponding to a rotation number 1/4 is obtained. Then, by the theory of normal form, we give theoretically the Arnold tongues in the weak resonances such that the system possesses two periodic orbits on the stable invariant closed curve generated from the Neimark–Sacker bifurcation. Furthermore, we obtain rigorously the parameter conditions under which the system has the chaotic behaviour in Marotto's sense. Finally, by numerical simulations, not only our results are verified, but also some new and interesting dynamical behaviours are discovered.

Dynamic behavior of multi-dimensional chaotic systems based on state variables and unknown parameters with applications in image encryption

Abstract To explore the impact of unknown terms and parameters on chaotic characteristics in chaotic systems, this paper examines the effects of state variables and unknown parameters. The study focuses on different combinations of linear, nonlinear, and constant terms It primarily investigates the role of multi-order state variables and their application to chaotic system models of varying dimensions. Firstly, by simulating a three-dimensional chaotic system, the paper analyzes how different combinations of nonlinear terms and initial conditions affect the system's chaotic behavior. Secondly, it evaluates the chaotic characteristics of a four-dimensional system, combining nonlinear terms with unknown parameters, using tools such as Lyapunov index diagrams, sample entropy, and dynamic trajectory plots. Finally, the paper integrates the constructed chaotic system with chaotic mapping to develop a two-level key chaotic image encryption system, thoroughly assessing its security and resistance to interference.

Optimizing Learning Path Design in Mobile Learning Platforms for Online Courses

With the rapid advancement of information technology, online education, particularly vocational education, has become a vital avenue for enhancing skills and knowledge. Vocational education necessitates flexible and personalized learning path design to accommodate the diverse needs and behaviors of learners. Mobile learning platforms, as a pivotal form of modern online education, provide learners with the convenience of accessing educational resources anytime and anywhere. However, existing methods for optimizing learning paths exhibit notable limitations, primarily in accurately capturing learners’ dynamic behaviors and in providing personalized and intelligent path design. Therefore, how to optimize learning paths based on learners’ dynamic behavior data has become a research hotspot in academia and educational practice. At present, many studies focus on matching analysis based on students’ static characteristics with course content but overlook learners’ behavioral changes and dynamic needs during the learning process. Traditional recommendation algorithms and rule-based path design methods are difficult to cope with complex learning behaviors and diverse learner needs. This study addresses these limitations by proposing an optimization model for mobile learning path design based on multi-view prediction of dynamic student behaviors. The model extracts mobile interaction features from student groups, constructs a multiple mobile behavior collaborative encoder, and employs multiple task label prediction techniques to achieve personalized and intelligent optimization of learning paths. The results demonstrate that this approach significantly enhances the learning efficiency and experience of learners, offering novel insights and technological support for the path design of mobile learning platforms.