Bifurcation Analysis and Chaos Control in a Discrete Epidemic System

The dynamics of discrete SI epidemic model, which has been obtained by the forward Euler scheme, is investigated in detail. By using the center manifold theorem and bifurcation theorem in the interior R+2, the specific conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation have been derived. Numerical simulation not only presents our theoretical analysis but also exhibits rich and complex dynamical behavior existing in the case of the windows of period-1, period-3, period-5, period-6, period-7, period-9, period-11, period-15, period-19, period-23, period-34, period-42, and period-53 orbits. Meanwhile, there appears the cascade of period-doubling 2, 4, 8 bifurcation and chaos sets from the fixed point. These results show the discrete model has more richer dynamics compared with the continuous model. The computations of the largest Lyapunov exponents more than 0 confirm the chaotic behaviors of the system x→x+δ[rN(1-N/K)-βxy/N-(μ+m)x], y→y+δ[βxy/N-(μ+d)y]. Specifically, the chaotic orbits at an unstable fixed point are stabilized by using the feedback control method

4α,6α-Dihy­droxy-1β-methyl­sulfonyl-8α,9α-ep­oxy-2β,12-epoxymethano-β-dihydro­agarofuran

The title mol­ecule, C16H24O8S, is a dihydro­agrofuran derivative and has a heteropolycyclic structure. One cyclohexane ring exhibits a chair conformation and the other a non-chair conformation. In the crystal structure there is an inter­molecular C—H⋯O hydrogen-bonding inter­action to stabilize the packing

Simulation of action potential propagation based on the ghost structure method

In this paper, a ghost structure (GS) method is proposed to simulate the monodomain model in irregular computational domains using finite difference without regenerating body-fitted grids. In order to verify the validity of the GS method, it is first used to solve the Fitzhugh-Nagumo monodomain model in rectangular and circular regions at different states (the stationary and moving states). Then, the GS method is used to simulate the propagation of the action potential (AP) in transverse and longitudinal sections of a healthy human heart, and with left bundle branch block (LBBB). Finally, we analyze the AP and calcium concentration under healthy and LBBB conditions. Our numerical results show that the GS method can accurately simulate AP propagation with different computational domains either stationary or moving, and we also find that LBBB will cause the left ventricle to contract later than the right ventricle, which in turn affects synchronized contraction of the two ventricles

PE-YOLO: Pyramid Enhancement Network for Dark Object Detection

Current object detection models have achieved good results on many benchmark datasets, detecting objects in dark conditions remains a large challenge. To address this issue, we propose a pyramid enhanced network (PENet) and joint it with YOLOv3 to build a dark object detection framework named PE-YOLO. Firstly, PENet decomposes the image into four components of different resolutions using the Laplacian pyramid. Specifically we propose a detail processing module (DPM) to enhance the detail of images, which consists of context branch and edge branch. In addition, we propose a low-frequency enhancement filter (LEF) to capture low-frequency semantics and prevent high-frequency noise. PE-YOLO adopts an end-to-end joint training approach and only uses normal detection loss to simplify the training process. We conduct experiments on the low-light object detection dataset ExDark to demonstrate the effectiveness of ours. The results indicate that compared with other dark detectors and low-light enhancement models, PE-YOLO achieves the advanced results, achieving 78.0% in mAP and 53.6 in FPS, respectively, which can adapt to object detection under different low-light conditions. The code is available at https://github.com/XiangchenYin/PE-YOLO.Comment: Accepted at ICANN 202