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In this paper, we propose an analytical approach to estimate the largest Lyapunov exponent (LLE) of a Rössler chaotic system, leveraging the synchronization method. This research focuses on establishing an analytical criterion for the synchronization of two identical Rössler chaotic systems through the linear coupling of state variables. This is crucial because the LLE of such systems can be estimated based on the critical coupling required for synchronization. Unlike previous studies, we first transform the synchronization error system between two identical Rössler chaotic systems into a set of Volterra integral equations by using the Laplace transform and convolution theorem. The critical coupling for synchronization is analytically derived using integral equation theory to solve the error system. As compared to the numerical results of the Rössler chaotic system's LLE, our analytical estimates demonstrate high accuracy. Our findings suggest that the challenge of estimating the Rössler chaotic system's LLE can be simplified to solving a cubic algebraic equation, offering a novel perspective on the analysis of how parameters influence the LLE's value in the Rössler chaotic system. [ABSTRACT FROM AUTHOR]

With the continuous evolution of the coronavirus, the Omicron variant has gradually replaced the Delta variant as the prevalent strain. Their inducing epidemics last longer, have a higher number of asymptomatic cases, and are more serious. In this article, we proposed a nonautonomous time-delayed susceptible-infected-removed (NATD-SIR) model to predict them in different regions of China. We obtained the maximum and its time of current infected persons, the final size, and the end time of COVID-19 epidemics from January 2022 in China. The method of the fifth-order moving average was used to preprocess the time series of the numbers of current infected and removed cases to obtain more accurate parameter estimations. We found that usually the transmission rate β (t) was a piecewise exponential decay function, but due to multiple bounces in Shanghai City, β (t) was approximately a piecewise quadratic function. In most regions, the removed rate γ (t) was approximately equal to a piecewise linear increasing function of (a*t+b)*H(t-k), but in a few areas, γ (t) displayed an exponential increasing trend. For cases where the removed rate cannot be obtained, we proposed a method for setting the removed rate, which has a good approximation. Using the numerical solution, we obtained the prediction results of the epidemics. By analyzing those important indicators of COVID-19, we provided valuable suggestions for epidemic prevention and control and the resumption of work and production. [ABSTRACT FROM AUTHOR]

Background Maternal exposure to pesticides during early pregnancy is associated with increased risks of birth defects, while the association between maternal exposure to chemical fertilizer during pregnancy and the risk of birth defects remains unknown. Methods Data were from a population-based birth defects surveillance system between 2007 and 2012 in Pingding County, Shanxi Province, northern China. A total of 14 074 births with 235 birth defects were used to estimate spatial clustering and correlations at the village level. A population-based case–control study of 157 cases with birth defects and 204 controls was performed to investigate the association between maternal chemical fertilizer exposure and the risk of birth defects by a two-level logistic model. Results The total prevalence of birth defects between 2007 and 2012 was 167.0/10 000 births. The spatial analysis indicated a remarkable high-risk area of birth defects in the southeast of Pingding County and the use of chemical fertilizer was associated with the risk of birth defects at the village level. After adjusting for confounders at the individual level, mothers who live in villages with chemical fertilizer application ≥65 tons/y had an increased risk of birth defects (adjusted odds ratio 2.06 [95% confidence interval 1.23 to 3.46]) compared with those of <65 tons/y. Conclusions Our findings suggest that the risk of birth defects may be associated with the use of chemical fertilizer in rural northern China. The findings must be cautiously interpreted and need to be investigated on larger samples. [ABSTRACT FROM AUTHOR]