The numerical approximation of exponential Euler method is constructed for semilinear stochastic differential equations SDEs. The convergence and mean-square MS stability of exponential Euler method are investigated. It is proved that the exponential Euler method is convergent with the strong order 1/2 for semilinear SDEs. A mean-square linear stability analysis shows that the stability region of exponential Euler method contains that of EM method and stochastic Theta method 0 ≤ θ < 1 and also contains that of the scale linear SDE, that is, exponential Euler method is analogue mean-square A-stable. Then the exponential stability of the exponential Euler method for scalar semi-linear SDEs is considered. Under the conditions that guarantee the analytic solution is exponentially stable in mean-square sense, the exponential Euler method can reproduce the mean-square exponential stability for any nonzero stepsize. Numerical experiments are given to verify the conclusions.
Recently, spacing policies of the vehicular platoon have been widely developed to enhance safety, traffic efficiency, and fuel consumption. However, the integrated spacing policies aim to maximum overall benefit, and the distributed spacing policies intense to get optimal monomer benefit. Ignoring the fairness of the benefit allocation of each vehicle will reduce the motivation to constitute the platoon. To fill this critical gap, this study proposes a spacing allocation method by treating spacing decisions as cooperative games. A flock’s model which is used to be the payoff function is introduced based on bionic motion principles. We present a characteristic function of the platoon for the cooperative game model considering the specific structure of the platoon. The τ value, Shapley value, and average lexicographic value are introduced and applied to allocate the spacing fairly. Proposed methods are compared with constant distance policy in some typical situations. The simulation results demonstrate that the spacing policy based on cooperative game theory improved the stable time for consistency control and the convergence of longitudinal following error.
So far, there has been no safe and convenient method to weigh the large fierce animals, like Amur tigers. To address this problem, we built models to predict the body weight of Amur tigers based on the fact that body weight is proportional to body measurements or age. Using the method of body measurements, we extracted the body measurements from 4 different kinds of the lateral body image of tigers, that is, total lateral image, central lateral image, ellipse fitting image, and rectangle fitting image, and then we respectively used artificial neural network (ANN) and power regression model to analyze the predictive relationships between body weight and body measurements. Our results demonstrated that, among all ANN models, the model built with rectangle fitting image had the smallest mean square error. Comparatively, we screened power regression models which had the smallest Akakai information criteria (AIC). In addition, using the method of age, we fitted nonlinear regression models for the relationship between body weight and age and found that, for male tigers, logistic model had the smallest AIC. For female tigers, Gompertz model had the smallest AIC. Consequently, this study could be applied to estimate body weight of captive, or even wild, Amur tigers safely and conveniently, helping to monitor individual health and growth of the Amur tiger populations.
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