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In this paper, a modified Leslie-type predator–prey system with Holling-type III functional response is formulated to investigate the dynamics in the presence of special Allee effect induced by fear factors. First, we calculate the first three focal values by the method of successor function to ensure that the system has an unstable weak focus of multiplicity 3. A focus- or center-type degenerate Bogdanov–Takens singularity of codimension 3 and a weak focus of multiplicity 1 or 2 together with a cusp of codimension 2 are derived for the system. Then multiple bifurcations are explored. It is shown that the system undergoes Hopf bifurcation of codimension 3 and hence three limit cycles are generated. There exists another large stable limit cycle enclosing these three limit cycles by Poincaré–Bendixson theorem. We demonstrate that a degenerate focus-type Bogdanov–Takens bifurcation of codimension 3 can occur by calculating the universal unfolding. It is also shown that a subcritical, supercritical or degenerate Hopf bifurcation occurs together with a Bogdanov–Takens bifurcation. Finally, numerical simulations are used to support the theoretical results. The analysis results reveal that the special Allee effect is beneficial for the persistence and diversity of ecosystem. [ABSTRACT FROM AUTHOR]

We study the bifurcation diagrams and exact multiplicity of positive solutions for the one-dimensional prescribed mean curvature equation −u′1+u′2′=λu1+up,−L0L,p\gt 0 are two evolution parameters. We prove that on the (λ,‖u‖∞)\left(\lambda ,\Vert u{\Vert }_{\infty })-plane, for 01p\gt 1, the bifurcation curve is reversed ε\varepsilon -like shaped bifurcation if L>L∗L\gt {L}^{\ast }, and is exactly decreasing for λ>λ∗\lambda \gt {\lambda }^{\ast } if 0

A knowledge graph is a repository that represents a vast amount of information in the form of triplets. In the training process of completing the knowledge graph, the knowledge graph only contains positive examples, which makes reliable link prediction difficult, especially in the setting of complex relations. At the same time, current techniques that rely on distance models encapsulate entities within Euclidean space, limiting their ability to depict nuanced relationships and failing to capture their semantic importance. This research offers a unique strategy based on Gibbs sampling and connection embedding to improve the model's competency in handling link prediction within complex relationships. Gibbs sampling is initially used to obtain high-quality negative samples. Following that, the triplet entities are mapped onto a hyperplane defined by the connection. This procedure produces complicated relationship embeddings loaded with semantic information. Through metric learning, this process produces complex relationship embeddings imbued with semantic meaning. Finally, the method's effectiveness is demonstrated on three link prediction benchmark datasets FB15k-237, WN11RR and FB15k. [ABSTRACT FROM AUTHOR]

The influences of Allee effect and density‐dependent mortality on population growth are of great significance in ecology. In this paper, we first consider a Gause‐type predator–prey model with simplified Holling type IV functional response, strong Allee effect on prey, and density‐dependent mortality of predator. It is shown that the system exhibits rich and complex dynamics like bistability, local and global bifurcations such as transcritical bifurcation, saddle‐node bifurcation, Hopf bifurcation, cusp bifurcation, Bogdanov–Takens bifurcation, Bautin bifurcation, homoclinic bifurcation, saddle‐node bifurcation of limit cycle, and heteroclinic bifurcation. Next, we separately explore the influences of Allee effect and density‐dependent mortality on the dynamics of the same model. The results show that the strong Allee effect induces the occurrence of heteroclinic bifurcation and the reduction of the number of limit cycles, while the density‐dependent mortality stabilizes the system. Since the analytical expressions of the interior equilibria are difficult to derive, the results are verified numerically. [ABSTRACT FROM AUTHOR]

In this paper, rich dynamics and complex bifurcations of an SIR epidemic model with saturated incidence rate and strong Allee effect are investigated. First, the existence of disease-free and endemic equilibria is explored, and we prove that the system has at most three positive equilibria, which exhibit different types such as hyperbolic saddle and node, degenerate unstable saddle (node) of codimension 2, degenerate saddle-node of codimension 3 at disease-free equilibria, and cusp, focus, and elliptic types Bogdanov–Takens singularities of codimension 3 at endemic equilibria. Second, bifurcation analysis at these equilibria are investigated, and it is found that the system undergoes a series of bifurcations, including transcritical, saddle node, Hopf, degenerate Hopf, homoclinic, cusp type Bogdanov–Takens of codimensional 2, and focus and elliptic type Bogdanov–Takens bifurcation of codimension 3 which are composed of some bifurcations with lower codimension. The system shows very rich dynamics such as the coexistence of multiple periodic orbits and homoclinic loops. Finally, numerical simulations are conducted on the theoretical results. [ABSTRACT FROM AUTHOR]

AbstractEpilepsy is a chronic brain disease caused by excessive discharge of brain neurons. Long-term recurrent seizures bring a lot of trouble to patients and their families. Prediction of different stages of epilepsy is of great significance. We extract pearson correlation coefficients (PCC) between channels in different frequency bands as features of EEG signals for epilepsy stages prediction. However, the features are of large feature dimension and serious multi-collinearity. To eliminate these adverse influence, the combination of traditional dimension reduction method principal component analysis (PCA) and logistic regression method with regularization term is proposed to avoid over-fitting and achieve the feature sparsity. The experiments are conducted on the widely used CHB-MIT dataset using different regularization terms L1 and L2, respectively. The proposed method identifies various stages of epilepsy quickly and efficiently, and it presents the best average accuracy of 94.86%, average precision of 96.71%, average recall of 93.48%, average kappa value of 0.90 and average Matthews correlation coefficient (MCC) value of 0.90 for all patients. [ABSTRACT FROM AUTHOR]

Traditional biological neural networks cannot simulate the real situation of the abrupt synaptic connections between neurons while modeling associative memory of human brains. In this paper, the memristive multidirectional associative memory neural networks (MAMNNs) with mixed time-varying delays are investigated in the sense of Filippov solution. First, three steps are given to prove the existence of the almost periodic solution. Two new lemmas are proposed to prove the boundness of the solution and the asymptotical almost periodicity of the solution by constructing Lyapunov function. Second, the uniqueness and global exponential stability of the almost periodic solution of memristive MAMNNs are investigated by a new Lyapunov function. The sufficient conditions guaranteeing the properties of almost periodic solution are derived based on the relevant definitions, Halanay inequality and Lyapunov function. The investigation is an extension of the research on the periodic solution and almost periodic solution of bidirectional associative memory neural networks. Finally, numerical examples with simulations are presented to show the validity of the main results. [ABSTRACT FROM AUTHOR]

Ground-glass nodules (GGN) are the main manifestation of early lung cancer, and accurate and efficient identification of ground-glass pulmonary nodules is of great significance for the treatment of lung diseases. In response to the problem of traditional machine learning requiring manual feature extraction, and most deep learning models applied to 2D image classification, this paper proposes a Transformer-based recognition model for ground-glass nodules from the view of global 3D asymmetry feature representation. Firstly, a 3D convolutional neural network is used as the backbone to extract the features of the three-dimensional CT-image block of pulmonary nodules automatically; secondly, positional encoding information is added to the extracted feature map and input into the Transformer encoder layer for further extraction of global 3D asymmetry features, which can preserve more spatial information and obtain higher-order asymmetry feature representation; finally, the extracted asymmetry features are entered into a support vector machine or ELM-KNN model to further improve the recognition ability of the model. The experimental results show that the recognition accuracy of the proposed method reaches 95.89%, which is 4.79, 2.05, 4.11, and 2.74 percentage points higher than the common deep learning models of AlexNet, DenseNet121, GoogLeNet, and VGG19, respectively; compared with the latest models proposed in the field of pulmonary nodule classification, the accuracy has been improved by 2.05, 2.05, and 0.68 percentage points, respectively, which can effectively improve the recognition accuracy of ground-glass nodules. [ABSTRACT FROM AUTHOR]

In this paper, a SEIR epidemic model related to media coverage and exogenous reinfections is established to explore the transmission dynamics of COVID-19. The basic reproduction number is calculated using the next generation matrix method. First, the existence of equilibrium points is investigated, and different kinds of equilibrium points indicate that the disease may disappear, or exist that result in different quantity of susceptible individuals, pre-symptomatic infected individuals and symptomatic infected individuals. The stability of the equilibria is discussed by a geometric approach, and it is found that controlling reproduction number to be lower than 1 is not sufficient for eradication of COVID-19. Second, transcritical bifurcation is explored, and it is found that improving the ratio of exogenous reinfection may lead to backward bifurcation under poor medical conditions, which indicates that two endemic equilibrium points appear. Third, to investigate the influence of parameters on the basic reproduction, sensitivity analysis is done to choose relatively sensitive parameters, and the parameters for treatment and media coverage are selected. An optimal control model is established to balance the treatment and media awareness. By exploring the existence and the uniqueness of the optimal control solution, the optimal control strategies are given. Finally, we run numerical simulations to verify the theoretical analysis on actual data of China, and the data from the four different states of India is used for forecasting the situation of infected individuals in a short period. It is found by the simulation that the co-function of treatment and media coverage results in the reduced number of infectious individuals. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of multistability of competitive neural networks with nonlinear, non‐monotonic piecewise activation functions and time‐varying delays. Several sufficient conditions are proposed to guarantee the existence of (2K+1)n$$ {\left(2K+1\right)}^n $$ equilibrium points and the locally exponential stability of (K+1)n$$ {\left(K+1\right)}^n $$ equilibrium points, where K$$ K $$ is a positive integer and determined by the property of activation functions and the parameters of neural networks. The quantitative relationship between the equilibrium points of the system and the zero roots of the bounding functions is given. In addition, the attraction basins of the exponentially stable equilibrium points are obtained. Finally, a numerical simulation is given to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]