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We consider a generalized Fisher-KPP equation with the growth function being time and space dependent in the form of “shifting with constant speed”. The main concerns are extinction and persistence, as well as spatial-temporal dynamics. By employing a new method relating to semigroup and some subtle estimates, we not only extend the main results in Li et al. [SIAM J. Appl. Math. 74 (2014), pp. 1397-1417] to a scenario when the growth function may have no sign change, but also improve the main results there by dropping some restrictions on the initial functions.

Detection of surface defects is an essential step to ensure the quality and reliability of rubber seal-ring products. Machine vision inspection methods have received attention from engineers because they are beneficial in terms of the detection speed or detection accuracy. It is important to simultaneously guarantee high speed and high accuracy of defect detection in practice production. Considering this problem, in this paper, we propose a YOLO-based (You Only Look Once) lightweight neural network with edge-attention fusion for defect detection of rubber rings. First, an edge-attention block is integrated into the network to improve the detection accuracy. The edge images are weighted with attention weights and summarized with feature maps in the block. Second, an involution-based feature pyramid structure is proposed to reduce the network size and computational cost by using a new involution operator, instead of a convolution operator, at the bottleneck of the feature pyramid. Comparison of the proposed network with popular YOLO networks was performed based on a rubber-ring-image dataset with 138 images. The network achieved the highest detection accuracy and fastest speed among selected lightweight networks, including YOLOv3-tiny, YOLOv5-s, and YOLOX-s. Moreover, compared with the large and highly accurate YOLOv3-spp network, the network size decreased by 93.45% and the computational cost decreased by 91.46%, while average precision only decreased by 3.41%. It can be concluded that the YOLO-based lightweight neural network reaches a good balance between detection speed and detection accuracy.

This paper is concerned with the forced traveling wave solution of a nonlocal dispersal Lotka-Volterra cooperation model under the habitat shifting with a constant speed. Particularly, we relax the condition of intrinsic production so that there may be no sign change. By constructing a pair of upper and lower solutions and using the method of monotone iteration, we prove the existence of traveling wave solution for any positive constant shifting speed.

This paper deals with the existence of traveling wave solutions of the Fisher equation with a shifting habitat representing a transition to a devastating environment. By constructing a pair of appropriate upper/lower solutions and using the method of monotone iteration, we prove that for any given speed of the shifting habitat edge, this reaction-diffusion equation admits a monotone traveling wave solution with the speed agreeing to the habitat shifting speed, which accounts for an extinction wave. This predicts not only how fast but also in what manner a biological species will die out in such a shifting habitat.

In this paper, we are concerned with existence/non-existence of traveling waves of a diffusive SIR epidemic model with general incidence rate of the form of f ( S ) g ( I ) and infinitely distributed latency but without demography. We show that the existence of traveling waves only depends on the basic reproduction number of the corresponding spatial-homogeneous system of delay differential equations, which is determined by the recovery rate, the local properties of f and g and a minimal wave speed c ∗ that is affected by the distributed delay. The proof of existence of traveling waves is by employing Schauder’s fixed point theorem, and the proof of nonexistence is completed with the aid of the bilateral Laplace transform.

In this study, we investigate the dynamic behavior on a system of neutral functional differential equations in critical case. Combining monotonicity techniques and functional methods, we develop the delicate monotonicity with the addressed system and show the convergence for every pre-compact solution with some initial condition, which improves and complements some existing ones.

Dealing with the epidemiological prey–predator is very important for us to understand the dynamical characteristics of population models. The existing literature has shown that disease introduction into the predator group can destabilize the established prey–predator communities. In this paper, we establish a new delayed SIS epidemiological prey–predator model with the assumptions that the disease is transmitted among the predator species only and different type of predators have different functional responses, viz. the infected predator consumes the prey according to Holling type-II functional response and the susceptible predator consumes the prey following the law of mass action. The positivity of solutions, the existence of various equilibrium points, the stability and bifurcation at those equilibrium points are investigated at length. Using the incubation period as bifurcation parameter, it is observed that a Hopf bifurcation may occur around the equilibrium points when the parameter passes through some critical values. We also discuss the direction and stability of the Hopf bifurcation around the interior equilibrium point. Simulations are arranged to show the correctness and effectiveness of these theoretical results.

A coupled system of nine identical cells with delays and𝔻3×𝔻3-symmetry is considered. The individual cells are modelled by a scalar delay differential equation which includes linear decay and nonlinear delayed feedback. By analyzing the corresponding characteristic equations, the linear stability of the equilibrium is given. We also investigate the simultaneous occurrence of multiple periodic solutions and spatiotemporal patterns of the bifurcating periodic oscillations by using the equivariant bifurcation theory of delay differential equations combined with representation theory of Lie groups. Numerical simulations are carried out to illustrate our theoretical results.

The delay time model (DTM) is widely used to model the two-stage failure process and is helpful for developing cost-effective inspection/maintenance plans. Imperfect maintenance is common in practice, but seldom considered in DTM. An improved DTM with imperfect maintenance at inspection has been developed based on the assumption of imperfect inspection maintenance and perfect failure maintenance. The model of the long-run availability for the improved DTM is established. Parameters estimation method and the test for goodness of fit method are given. Numerical simulations are performed to study the influence of imperfect maintenance on the long-run availability and to validate the credibility of the parameters estimation method. The results show that imperfect maintenance will decrease the long-run availability. The existence of the optimal inspection interval regarding the maximum long-run availability is tightly related to the improvement factor, which denotes the maintenance effect. The parameters estimation method proves credible. The maximum likelihood estimations of the reliability parameters can be easily achieved by the Genetic Algorithms (GAs) searching tool.

We consider a predator–prey system of Lotka–Volterra type with time delays and stage structure for prey. By analyzing the corresponding characteristic equations, the local stability of the equilibria is investigated and Hopf bifurcations occurring at the positive equilibrium under some conditions are demonstrated. The mathematical tools which enable us to obtain the sufficient conditions, guaranteeing the global asymptotical stability of the equilibria, are the well-known Kamke comparison theorem and an iteration technique. Numerical simulations are carried out to illustrate our theoretical results.

We consider a four-neuron ring with self-feedback and delays. By analyzing the associated characteristic equation, linear stability is investigated and Hopf bifurcations are demonstrated, as well as the stability and direction of the Hopf bifurcation are determined by employing the normal form method and the center manifold reduction. Numerical simulations are presented to illustrate the results.

In this paper, the inequality of boundedness for the multilinear fractional singular integral operators associated to the weighted Lipschitz functions is estimated. The operators include the Calderón-Zygmund singular integral operator and the fractional integral operator. MSC:42B20, 42B25.

This paper aims at studying the problem of the dynamics of switched Cohen-Grossberg neural networks with mixed delays by using Lyapunov functional method, average dwell time (ADT) method, and linear matrix inequalities (LMIs) technique. Some conditions on the uniformly ultimate boundedness, the existence of an attractors, the globally exponential stability of the switched Cohen-Grossberg neural networks are developed. Our results extend and complement some earlier publications.