The existence of periodic oscillation for a coupled FHN neural system with delays is investigated. Some criteria to determine the oscillations are given. Simple and practical criteria for selecting the parameters in this network are provided. Some examples are also presented to illustrate the result.

We consider the leader-following consensus problem of discrete-time multiagent systems on a directed communication topology. Two types of distributed observer-based consensus protocols are considered to solve such a problem. The observers involved in the proposed protocols include full-order observer and reduced-order observer, which are used to reconstruct the state variables. Two algorithms are provided to construct the consensus protocols, which are based on the modified discrete-time algebraic Riccati equation and Sylvester equation. In light of graph and matrix theory, some consensus conditions are established. Finally, a numerical example is provided to illustrate the obtained result.

We investigate the oscillation of the following higher order dynamic equation: $\{a_n(t)[(a_{n-\mathrm{1}}(t)(\cdots (a_{\mathrm{1}}(t)x^{\mathrm{\Delta }}(t){)}^{\mathrm{\Delta }}\cdots {)}^{\mathrm{\Delta }}{)}^{\mathrm{\Delta }}{]}^{\alpha }{\}}^{\mathrm{\Delta }}+p(t)x^{\beta }(t)=\mathrm{0}$, on some time scale $\mathit{T}$, where $n\ge \mathrm{2}$, $a_k(t)$ $\mathrm{}\mathrm{}(\mathrm{1}\le k\le n)$ and $p(t)$ are positive rd-continuous functions on $\mathit{T}$ and $\alpha ,\beta$ are the quotient of odd positive integers. We give sufficient conditions under which every solution of this equation is either oscillatory or tends to zero.

We investigate a class of multigroup epidemic models with general exposed distribution and nonlinear incidence rates. For a simpler case that assumes an identical natural death rate for all groups, and with a gamma distribution for exposed distribution is considered. Some sufficient conditions are obtained to ensure that the global dynamics are completely determined by the basic production number $R_0$. The proofs of the main results exploit the method of constructing Lyapunov functionals and a graph-theoretical technique in estimating the derivatives of Lyapunov functionals.

The concepts of $\alpha \omega$-remote neighborhood family, $\gamma \omega$-cover, and $\mathrm{L\omega }$-compactness are defined in $\mathrm{L\omega }$-spaces. The characterizations of $\mathrm{L\omega }$-compactness are systematically discussed. Some important properties of $\mathrm{L\omega }$-compactness such as $\omega$-closed heredity, arbitrarily multiplicative property, and preserving invariance under $\omega$-continuous mappings are obtained. Finally, the Alexander $\omega$-subbase lemma and the Tychonoff product theorem with respect to $\mathrm{L\omega }$-compactness are given.

This paper investigates the relationship between an unperturbed differential system and a perturbed differential system that have initial time difference. Notions of $h$-stability for differential systems with initial time difference are introduced, and stability criteria are formulated by using variation of parameter techniques.

We study the global asymptotic stability of the following difference equation: $x_{n+\mathrm{1}}=f(x_{n-k_{\mathrm{1}}},x_{n-k_{\mathrm{2}}},\dots ,x_{n-k_s};x_{n-m_{\mathrm{1}}},x_{n-m_{\mathrm{2}}},\dots ,x_{n-m_t}),n=\mathrm{0,1},\dots ,$ where and with $\{k_{\mathrm{1}},k_{\mathrm{2}},\dots ,k_s\}{\bigcap }_{\mathrm{‍}}\{m_{\mathrm{1}},m_{\mathrm{2}},\dots ,m_t\}=\mathrm{\varnothing },$ the initial values are positive, and $f\in C(E^{s+t},(\mathrm{0},+\mathrm{\infty }))$ with $E\in \{(\mathrm{0},+\mathrm{\infty }),[\mathrm{0},+\mathrm{\infty })\}$. We give sufficient conditions under which the unique positive equilibrium $\stackrel{-}{x}$ of that equation is globally asymptotically stable.

This work presents the fusion of integral channel features to improve the effectiveness and efficiency of pedestrian detection. The proposed method combines the histogram of oriented gradient (HOG) and local binary pattern (LBP) features by a concatenated fusion method. Although neural network (NN) is an efficient tool for classification, the time complexity is heavy. Hence, we choose support vector machine (SVM) with the histogram intersection kernel (HIK) as a classifier. On the other hand, although many datasets have been collected for pedestrian detection, few are designed to detect pedestrians in low-resolution visual images and at night time. This work collects two new pedestrian datasets—one for low-resolution visual images and one for near-infrared images—to evaluate detection performance on various image types and at different times. The proposed fusion method uses only images from the INRIA dataset for training but works on the two newly collected datasets, thereby avoiding the training overhead for cross-datasets. The experimental results verify that the proposed method has high detection accuracies even in the variations of image types and time slots.

We investigate the traveling wave solutions in a reaction-diffusion epidemic model. The existence of the wave solutions is derived through monotone iteration of a pair of classical upper and lower solutions. The traveling wave solutions are shown to be unique and strictly monotonic. Furthermore, we determine the critical minimal wave speed.

We investigate the periodic solutions of second-order difference problem with potential indefinite in sign. We consider the compactness condition of variational functional and local linking at 0 by introducing new number ${\lambda }_{\ast }$. By using Morse theory, we obtain some new results concerning the existence of nontrivial periodic solution.

This paper presents an image parsing algorithm which is based on Particle Swarm Optimization (PSO) and Recursive Neural Networks (RNNs). State-of-the-art method such as traditional RNN-based parsing strategy uses L-BFGS over the complete data for learning the parameters. However, this could cause problems due to the nondifferentiable objective function. In order to solve this problem, the PSO algorithm has been employed to tune the weights of RNN for minimizing the objective. Experimental results obtained on the Stanford background dataset show that our PSO-based training algorithm outperforms traditional RNN, Pixel CRF, region-based energy, simultaneous MRF, and superpixel MRF.

We consider the subharmonics with minimal periods for convex discrete Hamiltonian systems. By using variational methods and dual functional, we obtain that the system has a $pT$-periodic solution for each positive integer $p$, and solution of system has minimal period $pT$ as $H$ subquadratic growth both at 0 and infinity.

This paper investigates dynamical behaviors of the stochastic Hopfield neural networks with mixed time delays. The mixed time delays under consideration comprise both the discrete time-varying delays and the distributed time-delays. By employing the theory of stochastic functional differential equations and linear matrix inequality (LMI) approach, some novel criteria on asymptotic stability, ultimate boundedness, and weak attractor are derived. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.