Chaos, Solitons and Fractals: X最新文献

This study aims to identify the types of lineups based on their topological structure within a lineup network and to explore the relationship between lineup types and team standings during 10 NBA playoff seasons from 2012-2013 season to 2021-2022 season. A total of 15,699 lineups from 1,655 playoff games were collected to construct lineup networks. Three roles of the lineup, called core, connector and peripheral lineups, were found through community detection and unsupervised clustering of within-community degree, participation coefficient, and playing time. The percentage presence of connector lineups showed a positive correlation with the number of playoff wins (r = 0.45, p < 0.001), while peripheral lineups demonstrated a negative correlation (r = −0.33, p < 0.001). Additionally, the study found that connector lineups were more frequently reused than peripheral lineups (H = −14.90, p < 0.001) and that stronger teams exhibited lower conserved rates of all kinds of lineups. The collective performance was found to be more dependent on connector lineups (H = 926.42, p < 0.001) than peripheral lineups (H = 3342.63, p < 0.001). This study is the first to provide insights into the global lineup roles within season-scale lineup structures, offering generalizable suggestions for optimizing rotations. These suggestions advocate for the inclusion of more connector lineups and versatile players, and a reduction in the reuse rate of lineups, especially those classified as peripheral.

We investigated experimentally and theoretically the buildup of light pulses in an erbium-doped sub-MHz all-fiber laser modelocked by nonlinear polarization rotation. We were able to study the buildup of two different emission regimes: standard solitons and noise-like pulses. In each case, we were able to determine the round-trips required to achieve a stable emission state. Temporal traces and optical spectra of single pulses were measured along the start-up transient of the laser. The experimental results were also confirmed by numerical simulations. Under the specific conditions of this laser, the soliton regime takes about 400 round-trips to reach single-pulse emission. In the noise-like pulse regime, it takes only 20 round-trips for the characteristics of noise-like pulses to show up; although a more steady-state emission is reached also at about 400 round-trips.

Pandemics occur periodically worldwide. An accurate forecasting model is therefore essential to estimate the effect of the pandemic and plan accordingly. This research aims to provide a solution that could help the world predict the number of infection cases during pandemics and prepare to accommodate subsequent cases. The mathematical Multiplicative Holt–Winter (M-HW) model was improved regarding the data used to provide an accurate forecast. The model was applied to the Coronavirus (COVID-19) data, where COVID-19 is the recent pandemic that affected all nations worldwide since 2019. Two different periods in Saudi Arabia were modelled to estimate COVID-19 cases. Based on the daily confirmed cases in February 2023 and February 2022, the model showed accuracy of 99.51 % and 99.66 %, respectively. A MAPE value in February 2023 ranges between 0.015 and 1.07, while it ranges between 0.032 and 2.269 in February 2022. Additionally, the RMSE in February 2023 was 0.35, while in February 2022 it was 6.88. The model proved to be accurate and highly efficient. Thus, M-HW model is useful to forecast the number of cases in different regions in case of a pandemic, which makes a significant contribution to mitigating the spread of the virus minimizing the epidemiological spread impact on healthcare systems and focusing on managing and containing the epidemiological spread.

In this study, an approximation solution for a high-dimensional system in terms of the Caputo fractional derivative operator is obtained using the improved modified fractional Euler method, or IMFEM for short. To accomplish this aim, a result that can transform such a system into a double-equation, one-dimensional fractional-order system, is provided theoretically. Some physical applications, including fractional-order systems of equations of Emden–Fowler type, are discussed, and their graphs are plotted using MATLAB to demonstrate the IMFEM schema’s validity.

Hate speech, racism, and their co-existence are the human mind infections that are major factors that affect the living conditions of people, societal well-being, and political stability, economic and social disturbance throughout the world especially in underdeveloped nations of the world. The main objective of this study is to formulate and analyze the hate-speech and racism co-existence model with optimal control strategies and investigate the optimal effects of protection and improvement (rehabilitation) strategies to minimize and tackle the hate speech and racism co-existence dissemination in the community. In this study, we have computed the hate speech sub-model, the racism sub-model, and the hate speech and racism co-existence model equilibrium points and analyzed their stabilities, using the next generation operator approach all the models' effective reproduction numbers are computed, examined the phenomenon of backward bifurcation whenever the model effective reproduction number is less than one where at which both the positive co-existence free equilibrium point and the positive co-existence dominance equilibrium point exist simultaneously. To achieve the objective minimizing the hate speech and racism co-existence dissemination dynamics by implementing the efforts towards the protection and improvement (rehabilitation) strategies, the optimal control problem is re-formulated, and optimal control analysis is performed for the co-existence model using Pontryagin's maximum principle. Numerical simulations using MATLAB ode45 solver with fourth-order Runge-Kutta numerical methods to investigate the behavior of the co-existence model solutions and to explore the optimal effects of the protections and improvements (rehabilitation) strategies for the hate speech and racism co-existence dynamics are then performed. From the results, we observed that implementing the protection and improvement (rehabilitation) strategies simultaneously is the most effective approach to minimize and tackle the speech and racism co-existence propagation in the community.

This research aims to investigate the approximate controllability of multivalued impulsive stochastic fractional differential inclusions in Hilbert space with $\mathrm{ABC}$ fractional-order derivatives. First, we confirm the existence of mild solutions for the proposed control system using stochastic analysis, resolvent operator theory, and the fixed point technique. Secondly, we discuss a new set of sufficient conditions for the approximate controllability of the systems. The results are obtained under the assumption that the associated linear system is approximately controllable. Finally, an example is provided to illustrate the obtained results.

We investigate the dynamics of active rotator systems by the moment closure method based on matching derivatives. This method is illustrated and verified in terms of three systems: the single-element rotator, the two coupled rotators and the mean field coupled rotators. Using the moment closure method, we study the effect of common noise on active rotator systems from the perspective of stochastic resonance. It is shown that the noise-induced stochastic resonance and parameter-induced stochastic resonance occur in the above three systems. Our observation discloses that the two kinds of stochastic resonance effect can be enhanced by both increasing coupling strength and the number of coupled rotators.

The Helmholtz-Duffing equation with the Caputo fractional order derivative will be introduced in this article. We employ the fixed point theory to establish the existence and uniqueness results and prove the Hyers-Ulam stability. Drone applications for controlling the synthesis of external forces in torque, angular velocity, and projection served as a source of motivation. In the end, we developed numerical simulations to support our theoretical findings.

In this paper, we investigate the stability analysis of the equilibrium points and the influence of the orientation on the suppression of chaotic behavior of the generalized Lorenz system proposed. A three-dimensional system model is obtained using the spectral method. We proved that the first equilibrium point is globally asymptotically stable and the other two equilibria are asymptotically stable under certain conditions on the control parameters σ, P, r, $b_1$ and $b_2$. These theoretical results are supported by numerical simulations. Also, we showed that chaos can be suppressed by a boundary crisis or period-doubling by choosing an appropriate tilt angle. Bifurcation diagrams are drawn to confirm these results.

Plutella xylostella, commonly called Diamondback moth (DBM), a highly destructive and rapidly spreading agricultural pest originally from Europe. This pest poses a significant threat to global food security, with estimates suggesting that periodic outbreaks of Diamondback moth lead to annual crop losses of up to $US $4-5$ billion worldwide. Given the potential for such substantial losses, it is crucial to employ various methods and techniques to understand the factors affecting the interaction between Diamondback moths and cabbage plants, which, in turn, impact cabbage biomass. In this paper, we propose a deterministic ecological model to capture the dynamics of Plutella xylostella infestations in cabbage biomass. The model is designed based on the life cycle stages of the pest, aiming at targeting the specific stage effectively. The synthetic data is generated using Least Square Algorithm through addition of Gaussian noise into numerically obtained values from existing literature to simulate real-world data. Global sensitivity analysis was done through Latin Hypercube sampling, highlights the significance of parameters such as $\psi ,{\alpha }_E$ and δ positively influence the growth of the diamondback moth in a cabbage biomass. In light of these findings, the study proposes that control strategies should be specifically directed towards these sensitive parameters. By doing so, we mitigate the pest population and enhance cabbage production.