Chaos, Solitons and Fractals: X最新文献

The generation of high-order rogue waves (RWs) without the exact solution is an intriguing subject that has not yet been fully explored, especially for the third-order RWs. In this paper, we investigate the collision dynamics in a three-component Bose–Einstein condensate (BEC), and propose a scheme capable of generating such high-order RWs, such as second- and third-order RWs. The results show that the peaks of the three first-order RWs coincide in time and space when the third-order RWs are excited during the collision. Furthermore, by controlling the offsets of initial wavepackets and intraspecific interaction coefficients within the BEC, the collision behavior of RWs can be precisely manipulated. Compared to two-component BECs, these three-component collisions exhibit more diverse structures for exciting RW phenomena.

Riccati’s differential equation is formulated as abstract equation in finite or infinite dimensional Banach spaces. Since the Riccati’s differential equation with the Cole–Hopf transform shows a relation between the first order evolution equations and the second order evolution equations, its generalization suggests the existence of recurrence formula leading to a sequence of differential equations with different order. In conclusion, by means of the logarithmic representation of operators, a transform between the first order evolution equations and the higher order evolution equation is presented. Several classes of evolution equations with different orders are given, and some of them are shown as examples.

The aim of this paper is to explore finite-time synchronization in a specific subset of fractional-order epidemic reaction–diffusion systems. Initially, we introduce a new lemma for finite-time stability, which extends existing criteria and builds upon previous discoveries. Following this, we design effective state-dependent linear controllers. By utilizing a Lyapunov function, we derive new sufficient conditions to ensure finite-time synchronization within a predefined time frame. Lastly, we present numerical simulations to demonstrate the applicability and effectiveness of the proposed technique.

Unemployment is a major problem worldwide and is one of the key factors determining a nation’s economic status. The issue of unemployment is made more difficult globally by the ongoing rise in labor force participation and the scarcity of job positions. In this work, we study the unemployment model with two distinct fractional-order derivatives: the Caputo operator and the Atangana–Baleanu operator in the sense of Caputo (ABC). These derivatives under consideration are the operators widely utilized in modeling real-world phenomena in fractional dynamics. The existence and uniqueness of the solutions to the fractional model under consideration are ascertained using the fixed-point theory. The Hyers-Ulam analysis is employed to determine stability. For the numerical results, we present an Adams-type predictor–corrector (PC) technique for Caputo derivative and an extended Adams Bashforth (ABM) method for Atangana–Baleanu derivative. The outcomes achieved with the Atangana–Baleanu–Caputo and Caputo derivatives are identical to those of the regular case when fractional order $\nu =1.00$. However, the results obtained change slightly as fractional order assumes values smaller than one, and this variation becomes most noticeable when the fractional order $\nu <0.72$. This is because of the fractional derivative definitions’ underlying kernel. It is shown that the Mittag–Leffler kernel derivative provides better results for smaller fractional orders.

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.