Search Results (107)

This paper presents a novel four-dimensional autonomous conservative model characterized by an infinite set of equilibrium points and an unusual algebraic structure in which all eigenvalues of the Jacobian matrix are zero. The linearization of the proposed model implies that classical stability analysis is inadequate, as only the center manifolds are obtained. Consequently, the stability of the system is investigated through both analytical and numerical methods using Lyapunov functions and numerical simulations. The proposed model exhibits rich dynamics, including hyperchaotic behavior, which is characterized using the Lyapunov exponents, bifurcation diagrams, sensitivity analysis, attractor projections, and Poincaré map. Moreover, in this paper, we explore the model with fractional-order derivatives, demonstrating that the fractional dynamics fundamentally change the geometrical structure of the attractors and significantly change the system stability. The Grünwald–Letnikov formulation is used for modeling, while numerical integration is performed using the Caputo operator to capture the memory effects inherent in fractional models. Finally, an analog electronic circuit realization is provided to experimentally validate the theoretical and numerical findings. Full article

This work focuses on characterizing structured metamaterials by assessing their elastic law and ultimate strength using finite elements and limit analysis applied to a representative volume element. The elastic and plastic behavior of a reference geometry—the octet truss lattice—is obtained by calculating the response of the representative volume element subjected to prescribed tensor strain bases, namely pure normal strain and pure shear, along the cube symmetry directions. The geometry of the body centered cubic and pure cubic phases of the representative volume element has been analyzed, highlighting that the elastic isotropic behavior depends on the ratio between the stiffnesses of the two phases. The ultimate behavior of the structure has been analyzed through the direct application of the lower bound method of limit analysis. The method has been implemented in a direct finite element environment using the limit analysis procedure developed by the authors. The method was already used and described in previous publications and is briefly recalled. It is based on the identification of the linear operator linking the self-equilibrated stress set to a discrete parameter manifold, accounting for the piecewise continuous distribution of the permanent strain. In the paper, it is highlighted that for different aspect ratios between the body-centered cubic and the pure cubic phase geometry, different ratios between limit shear stress and normal stress arise, the isotropic one assumed to coincide with the von Mises result, where ${\displaystyle \frac{{\sigma }_0}{{\tau }_0}}=\sqrt{3}$. Full article

We explore chaos, local dynamics, codimension-one, and codimension-two bifurcations of an asymmetric discrete predator–prey model. More precisely, for all the model’s parameters, it is proved that the model has two boundary fixed points and a trivial fixed point, and also under parametric conditions, it has an interior fixed point. We then constructed the linearized system at these fixed points. We explored the local behavior at equilibria by the linear stability theory. By the series of affine transformations, the center manifold theorem, and bifurcation theory, we investigated the detailed codimensions-one and two bifurcations at equilibria and examined that at boundary fixed points, no flip bifurcation exists. Furthermore, at the interior fixed point, it is proved that the discrete model exhibits codimension-one bifurcations like Neimark–Sacker and flip bifurcations, but fold bifurcation does not exist at this point. Next, for deeper understanding of the complex dynamics of the model, we also studied the codimension-two bifurcation at an interior fixed point and proved that the model exhibits the codimension-two 1:2, 1:3, and 1:4 strong resonances bifurcations. We then investigated the existence of chaos due to the appearance of codimension-one bifurcations like Neimark–Sacker and flip bifurcations by OGY and hybrid control strategies, respectively. The theoretical results are also interpreted biologically. Finally, theoretical findings are confirmed numerically. Full article

In this paper, we investigate the nonlinear dynamic behavior of a cart–double pendulum system with single time delay feedback control. Based on the center manifold theorem and stochastic averaging method, a reduced-order dynamic model of the system is established, with a focus on analyzing the influence of time delay parameters and stochastic excitation on the system’s Hopf bifurcation characteristics. By introducing stochastic differential equation theory, the system is transformed into the form of an Itô equation, revealing bifurcation phenomena in the parameter space. Numerical simulation results demonstrate that decreasing the time delay and increasing the time delay feedback gain can effectively enhance system stability, whereas increasing the time delay and decreasing the time delay feedback gain significantly improves dynamic performance. Additionally, it is observed that Gaussian white noise intensity modulates the bifurcation threshold. This study provides a novel theoretical framework for the stochastic stability analysis of time delay-controlled multibody systems and offers a theoretical basis for subsequent research. Full article

Exhaust manifolds accumulate creep and fatigue damage under cyclic thermal loading, leading to localized failure. Understanding a material’s mechanical behavior is crucial for accurate life assessment. This study systematically investigated the low-cycle fatigue (LCF) and creep–fatigue interaction behaviors of medium-silicon molybdenum ductile iron. It was found that QTRSi4Mo exhibited cyclic hardening at room temperature and 400 °C, whereas it exhibited cyclic softening at 600 °C and 700 °C for low-cycle stress–strain responses. During creep–fatigue tests with hold time, variations in the strain amplitude did not alter the hysteresis loop shape or the hardening/softening characteristics of the material. They only induced a slight upward shift in the yield center. Additionally, stress relaxation primarily occurred in the initial phase of the hold period, so the hold duration had little effect on the final stress value. The investigation of creep–fatigue life models highlighted that accurately characterizing the damage induced by stress relaxation during the hold stage is critical for creep damage evaluation. The calculated creep damage results differed greatly from the experimental results of the time fraction model (TF). A combined approach using the strain energy density dissipation model (T-SEDE) and the Ostergren method demonstrated excellent predictive capability for creep–fatigue life. Full article

This paper studies the effects of resource limitations, immunity decay, and delays on an Ebola epidemic model and an optimal control strategy. The model includes two types of delays: a delay in the incubation period of infected individuals and a delay in treatment. Conditions for a Hopf bifurcation at the endemic equilibrium are verified, with its direction and stability analyzed via normal form theory and the center manifold theorem. We also studied the optimal control problem for the SIRD delay model using educational campaigns and Ebola survivors’ immunity as control variables. Furthermore, we formulate an optimization problem based on Pontryagin’s maximum principle. This problem uses a modified Runge-Kutta approach with delays to discover the best control strategy to reduce infections and intervention costs. Finally, simulation results confirm analytical conclusions and show the practical implications of the optimum Ebola control plan using the dde23 MATLAB R2024a built-in solver and DDE-Biftool. Full article

In recent decades, few-shot object detection in SAR imagery has gained prominence as a major research focus. The unique imaging mechanism of SAR causes the model to suffer from foreground–background imbalance and inaccurate extraction of class prototypes for novel class instances. Therefore, we propose an innovative few-shot object detection algorithm for SAR images via context-aware and robust Gaussian flow representation. First, we design the Context-Aware Enhancement module to address the foreground–context imbalance problem by refining representative support features into fine-grained prototypes, which are deeply fused with query features based on the prototype matching paradigm. Second, we devise the Manifold Class Distribution Estimation module to address the difficulty of class distribution estimation and the fluctuation of class centers of the sparse novel class. Furthermore, we formulate the Category-Balanced Difference Aggregation module to model the relationship between the base class and the novel class, addressing the sensitivity of the model to the variance of the novel class instances. Finally, we design the Cosine Decoupling Module so that the aggregated features are executed only on the classification branch without affecting the precise localization of the target. Experiments based on SAR-AIRcraft-1.0 and the self-constructed MSAR-AIR dataset indicate that the fine-grained detection and identification performance of the novel class of airplanes can reach 32.90% and 55.26%, respectively, in the 10-shot and 50-shot cases. In addition, our method enables cross-domain detection for different scenarios and sample types and exhibits excellent generalization performance in data-sparse scenarios. Full article

The Basener and Ross mathematical model is widely recognized for its ability to characterize the interaction between the population dynamics and resource utilization of Easter Island. In this study, we develop and investigate a discrete-time version of the Basener and Ross model. First, the existence and the stability of fixed points for the present model are investigated. Next, we investigated various bifurcation scenarios by establishing criteria for the occurrence of different types of codimension-one bifurcations, including flip and Neimark–Sacker bifurcations. These criteria are derived using the center manifold theorem and bifurcation theory. Furthermore, we demonstrated the existence of codimension-two bifurcations characterized by 1:2, 1:3, and 1:4 resonances, emphasizing the model’s complex dynamical structure. Numerical simulations are employed to validate and illustrate the theoretical predictions. Finally, through bifurcation diagrams, maximal Lyapunov exponents, and phase portraits, we uncover a diversity of dynamical characteristics, including limit cycles, periodic solutions, and chaotic attractors. Full article

This paper investigates the dynamical behavior of a discrete fractional-order modified Leslie–Gower model with a Michaelis–Menten-type harvesting mechanism and a Holling-II functional response. We analyze the existence and stability of the nonnegative equilibrium points. For the interior equilibrium points, we study the conditions for period-doubling and Neimark–Sacker bifurcations using the center manifold theorem and bifurcation theory. To control the chaos arising from these bifurcations, two chaos control strategies are proposed. Numerical simulations are performed to validate the theoretical results. The findings provide valuable insights into the sustainable management and conservation of ecological systems. Full article

In this paper, we aim to solve the issue of pattern formation mechanisms in a spatiotemporally discrete activator–inhibitor model that incorporates self- and cross-diffusions. We seek to identify the conditions that lead to the emergence of complex patterns and to elucidate the principles governing the dynamic behaviors that result in these patterns. We first construct a corresponding coupled map lattice (CML) model based on the continuous activator–inhibitor reaction–diffusion system. In the reaction stage, we examine the existence, uniqueness, and stability of the homogeneous stationary state and specify the parametric conditions for realizing these properties. Furthermore, by applying the center manifold theorem, we perform a flip bifurcation analysis and confirm that the model is capable of undergoing flip bifurcation. In the diffusion stage, we focus on the analysis of Turing bifurcation and determine the parameter conditions for the emergence of Turing instability. Through numerical simulations, we validate and explain the results of our theoretical analysis. Our study reveals various Turing instability mechanisms by coupling Turing and flip bifurcations, which include pure-self-diffusion-Turing instability, pure-cross-diffusion-Turing instability, flip-self-diffusion-Turing instability, flip-cross-diffusion-Turing instability, and chaos-self-diffusion-Turing instability mechanisms. Under different mechanisms, we illustrate the corresponding Turing patterns and discover a rich variety of pattern types such as labyrinthine, mosaic, alternating mosaic, colorful mottled grid patterns with winding and twisted bands, and patterns with dense patches and twisted bands nested together. Our research provides a theoretical framework and numerical support for understanding the complex dynamical behaviors and pattern formations in activator–inhibitor models with self- and cross-diffusions. Full article

In healthcare, vast amounts of data are increasingly collected through sensors for smart health applications and patient monitoring or diagnosis. However, such medical data often comprise sensitive patient information, posing challenges regarding data privacy, and are resource-intensive to acquire for significant research purposes. In addition, the common case of lack of information due to technical issues, transcript errors, or differences between descriptors considered in different health centers leads to the need for data imputation and partial data generation techniques. This study introduces a novel methodology for partially synthetic tabular data generation, designed to reduce the reliance on sensor measurements and ensure secure data exchange. Using the UMAP (Uniform Manifold Approximation and Projection) visualization algorithm to transform the original, high-dimensional reference data set into a reduced-dimensional space, we generate and validate synthetic values for incomplete data sets. This approach mitigates the need for extensive sensor readings while addressing data privacy concerns by generating realistic synthetic samples. The proposed method is validated on prostate and breast cancer data sets, showing its effectiveness in completing and augmenting incomplete data sets using fully available references. Furthermore, our results demonstrate superior performance in comparison to state-of-the-art imputation techniques. This work makes a dual contribution by not only proposing an innovative method for synthetic data generation, but also studying and establishing a formal framework to understand and solve synthetic data generation and imputation problems in sensor-driven environments. Full article

Impetigo is a highly contagious skin infection that primarily affects children and communities in low-income regions and has become a significant public health issue impacting both individuals and healthcare systems. A nonlinear deterministic model based on the transmission dynamics of skin sores (impetigo) is developed with a specific emphasis on the time delay effects in the infection and recovery processes. To address this complexity, we introduce a delay differential equation (DDE) to describe the dynamic process. We analyzed the existence of Hopf bifurcations associated with the two equilibrium points and examined the mechanisms underlying the occurrence of these bifurcations as delays exceeded certain critical values. To obtain more comprehensive insights into this phenomenon, we applied the center manifold theory and the normal form method to determine the direction and stability of Hopf bifurcations near bifurcation curves. This research not only offers a novel theoretical perspective on the transmission of impetigo but also lays a significant mathematical foundation for developing clinical intervention strategies. Specifically, it suggests that an increased time delay between infection and isolation could lead to more severe outbreaks, further supporting the development of more effective intervention approaches. Full article

Playgrounds are envisaged as spaces designed to provide a safe and enjoyable environment that facilitates physical activity among children and adolescents. However, in various instances within cities formerly under socialist governance, these playgrounds have suffered neglect and lacked maintenance, coherent conceptual frameworks, professional oversight, suitable materials for playground structures, and attention to vegetation or potentially toxic elements. They became residual areas in the city’s built environment. Presently, the evaluation and the regeneration of playgrounds in cities have emerged as a significant task. Amidst the densely populated urban fabric, these spaces hold considerable importance for outdoor activities, social interaction, recreational pursuits, and the healthy development of future generations. Simultaneously, these places can play a crucial role in a city’s green infrastructure, local landscapes, and the challenges of sustainability prompted by climate change. The landscape analysis of 22 playgrounds classified them based on land use characteristics, location, functions, equipment, quality, and accessibility. A case study in Târgu-Mureș, scrutinized in detail within this analysis due to its proximity to the city center, within a densely populated urban area, and its multifaceted functionalities, underscores the need for a comprehensive approach encompassing diverse disciplines to address its manifold usage requirements. Full article

On 1–3 May 2023, severe hydro-meteorological events occurred in the Italian Emilia-Romagna region. Such events caused extensive flooding, landslides, isolation of many areas, evacuation of many families, and severe damage to infrastructure, agriculture, buildings, and essential services. Several municipalities were affected, thousands of civilians had to be evacuated, and losses of life occurred. The consequences beyond the recorded immediate impacts on infrastructure and life were impressive, and extended to the regional economy, specifically in the Fruit Valley, where, in addition to immediate yield losses, long-term damage to orchard production is expected due to persistent flooding. The civil and cultural building heritage has also been heavily affected, both in the countryside and in inhabited centers. Some of the damage, direct and indirect, caused by flooding on buildings will also see an evolution in the medium- to long-term that needs to be addressed. This paper analyzes the manifold aspects of such an atmospheric phenomenon and its impacts to understand the potential increasing occurrence of similar events in the climate change context. Full article

This paper presents an innovative approach using Dynamical Systems Theory (DST) for interplanetary orbit insertion into Saturn−Titan three−body orbits. By leveraging DST, this study identifies invariant manifolds guiding a spacecraft into Titan−centered Distant Retrograde Orbits (DROs), strategically selected for their scientific significance. Subsequently, Particle Swarm Optimization (PSO) is employed to fine−tune the insertion parameters, thereby minimizing ΔV. The results demonstrate that the proposed method allows for a reduction in ΔV of over 70% compared to conventional approaches like patched conics−based flybys (2.68 km/s vs. 9.23 km/s), albeit with an extended time of flight, which remains notably faster than weak stability boundary transfers. This paper serves as an interplanetary mission planning methodology to optimize spacecraft trajectories for the exploration of the Saturn−Titan system. Full article