The aim of this paper is to investigate the dynamical behaviour of a class of three species Lotka–Volterra competitive-competitive–cooperative models with feedback controls and time delays. By developing a new analysis technique, we obtain some sufficient conditions that ensure these models have the dynamical property of permanence. We also give some sufficient conditions that guarantee the global attractivity of positive solutions for this system by constructing a new suitable Lyapunov function. Finally, we give some numerical simulations to illustrate our results in this paper.

In this paper, a tracking algorithm based on the residual neural network model and machine learning is proposed. Compared with the widely used VGG network, the residual neural network has deeper characteristic layers and special additional layer structure, which break the symmetry of the network and reduce the degradation of the neural network. The additional layer and convolution layer are used for feature fusion to represent the target. The multi-features of the object can be captured by using the developed algorithm, so that the accuracy of tracking can be improved in some complex scenarios. In addition, we defined a new measure to calculate the similarity of different image regions and find the optimal matched region. The search area is delimited according to the continuity of the target motion, which improves the real-time performance of tracking. The experimental results illustrate that the proposed algorithm achieved a higher accuracy while taking into account the real time performance, especially in dealing with some complex scenarios such as deformation, rotation changes and background clutters, in comparison with the Multi-Domain Network (MDNet) algorithm based on a convolutional neural network.

In this paper, we consider the exact solutions of the complex cubic-quintic Ginzburg–Landau equation. By investigating the dynamical behavior of solutions of the corresponding traveling wave system of this PDE, we derive exact explicit parametric representations of the periodic wave solutions under given parameter conditions.

In this paper, we investigate the generalized Radhakrishnan–Kundu–Lakshmanan equation with polynomial law using the method of dynamical systems. By using traveling-wave transformation, the model can be converted into a singular integrable traveling-wave system. Then, we discuss the dynamical behavior of the associated regular system and we obtain bifurcations of the phase portraits of the traveling-wave system under different parameter conditions. Finally, under different parameter conditions, we obtain the exact periodic solutions, and the peakon, homoclinic and heteroclinic solutions.

In this paper, we consider the nonlinear Schrödinger’s equation with Kudryashov’s law of refractive index. By using the method of dynamical systems, we obtain bifurcations of the phase portraits of the traveling wave system under different parameter conditions. Corresponding to some special level curves, we derive possible exact explicit parametric representations of solutions (including peakon, periodic peakon, solitary wave solutions and compactons) under different parameter conditions.