We study a Lotka-Volterra type predator-prey model with a transmissible disease in the predator population. We concentrate on the effect of diffusion and cross-diffusion on the emergence of stationary patterns. We first show that both self-diffusion and cross-diffusion can not cause Turing instability from the disease-free equilibria. Then we find that the endemic equilibrium remains linearly stable for the reaction diffusion system without cross-diffusion, while it becomes linearly unstable when cross-diffusion also plays a role in the reaction-diffusion system; hence, the instability is driven solely from the effect of cross-diffusion. Furthermore, we derive some results for the existence and nonexistence of nonconstant stationary solutions when the diffusion rate of a certain species is small or large.

Diverse movement patterns may be identified when we study a set of moving entities. One of these patterns is known as a V-formation for it is shaped like the letter V. Informally, a set of entities shows a V-formation if the entities are located on one of their two characteristic lines. These lines meet in a position where there is just one entity considered the leader of the formation. Another movement pattern is known as a circular formation for it is shaped like a circle. Informally, circular formations present a set of entities grouped around a center in which the distance from these entities to the center is less than a given threshold. In this paper we present a model to identify V-formations and circular formations with outliers. An outlier is an entity which is part of a formation but is away from it. We also present a model to identify doughnut formations, which are an extension of circular formations. We present formal rules for our models and an algorithm for detecting outliers. The model was validated with NetLogo, a programming and modeling environment for the simulation of natural and social phenomena.

A set of easily verifiable sufficient conditions are derived to guarantee the existence and the global stability of positive periodic solutions for two-species competitive systems with multiple delays and impulses, by applying some new analysis techniques. This improves and extends a series of the well-known sufficiency theorems in the literature about the problems mentioned previously.

There is a close link between the number of suppliers and the quality of products including service. However, there is a research gap in this field. Particularly, the problem whether this link would be affected by different supply chain profit distribution policies is lack of in-depth research. In this paper, a basic game model for quality supervision game without FLSPs’ competition (Model I) in a logistics service supply chain (LSSC) is established first. Model I adopts a mixed payment contract and is composed of a logistics service integrator (LSI) and functional logistics service provider (FLSP). The mixed-strategy Nash equilibrium of Model I is presented. Model II considering competition among FLSPs is then built based on Model I, and the new mixed-strategy Nash equilibrium is provided. Results show that under competition the ordinary mixed payment contract cannot make quality supervision game parameters all optimized. Therefore, Model III under a compensation mechanism is established based on Model II, and the range of the compensation value is calculated. Furthermore, we propose three kinds of concrete compensation mechanisms, which are fixed, linear, and nonlinear compensation mechanism. And the optimal compensation mechanism for a LSI with different numbers of FLSPs is provided.

Environmental protection is becoming more and more important for enterprises because of stronger public awareness, competitors and communities, and government regulations. For this purpose, some programs have become more popular for raising environmental awareness including total quality environmental management and green supply chain management. Reducing the environmental pollution from upstream to downstream during procuring raw materials, producing, distribution, selling products, and products depreciation is the most important goal of Green Supply Chain Management (GSCM). The main contribution of this study is introducing the main factors in green supply chain management that are very important in environmental attributes by providing an evaluation framework to select the most eligible green suppliers by examining the influential and important criteria and subcriteria among ten elements of two main GSCM practices, namely, green logistics and environmental protection. First, these factors are divided into two groups, that is, green logistics and environmental protection, and then by applying DEMATEL technique, the complex causal relationship between all factors dependencies and feedbacks among them is examined. Finally, by drawing the impact relationship map the most important and influential factors are determined for improving green supply chain environmental aspects.

Recent psychological research indicates that consumers that search exhaustively for the best option of a market product—known as maximizers—eventually feel worse than consumers who just look for something good enough—called satisficers. We formulate a time allocation model to explore the relationship between different distributions of prices of the product and the satisficing behavior and the related welfare of the consumer. We show numerically that, as the number of options becomes large, the maximizing behavior produces less and less welfare and eventually leads to choice paralysis—these are effects of choice overload—whereas satisficing conducts entail higher levels of satisfaction and do not end up in paralysis. For different price distributions, we provide consistent evidence that maximizers are better off for a low number of options, whereas satisficers are better off for a sufficiently large number of options. We also show how the optimal satisficing behavior is affected when the underlying price distribution varies. We provide evidence that the mean and the dispersion of a symmetric distribution of prices—but not the shape of the distribution—condition the satisficing behavior of consumers. We also show that this need not be the case for asymmetric distributions.

Nowadays, swarm robotics research is having a great increase due to the benefits derived from its use, such as robustness, parallelism, and flexibility. Unlike distributed robotic systems, swarm robotics emphasizes a large number of robots, and promotes scalability. Among the multiple applications of such systems we could find are exploring unstructured environments, resource monitoring, or distributed sensing. Two of these applications, monitoring, and perimeter/area detection of a given resource, have several ecological uses. One of them is the detection and monitoring of pollutants to delimit their perimeter and area accurately. Maritime activity has been increasing gradually in recent years. Many ships carry products such as oil that can adversely affect the environment. Such products can produce high levels of pollution in case of being spilled into sea. In this paper we will present a distributed system which monitors, covers, and surrounds a resource by using a swarm of homogeneous low cost drones. These drones only use their local sensory information and do not require any direct communication between them. Taking into account the properties of this kind of oil spills we will present a microscopic model for a swarm of drones, capable of monitoring these spills properly. Furthermore, we will analyse the proper macroscopic operation of the swarm. The analytical and experimental results presented here show the proper evolution of our system.

Analytic hierarchy process (AHP) is a leading multi-attribute decision-aiding model that is designed to help make better choices when faced with complex decisions involving several dimensions. AHP, which enables qualitative analysis using a combination of subjective and objective information, is a multiple criteria decision analysis approach that uses hierarchical structured pairwise comparisons. One of the drawbacks of AHP is that a pairwise comparison cannot be completed by an actor or stakeholder not fully familiar with all the aspects of the problem. The authors have developed a completion based on a process of linearization that minimizes the matrix distance defined in terms of the Frobenius norm (a strictly convex minimization problem). In this paper, we characterize when an incomplete, positive, and reciprocal matrix can be completed to become a consistent matrix. We show that this characterization reduces the problem to the solution of a linear system of equations—a straightforward procedure. Various properties of such a completion are also developed using graph theory, including explicit calculation formulas. In real decision-making processes, facilitators conducting the study could use these characterizations to accept an incomplete comparison body given by an actor or to encourage the actor to further develop the comparison for the sake of consistency.

This paper aimed to address the study of a new family of anomalies, called natural anomalies, defined as a one-parameter convex linear combination of the true and secondary anomalies, measured from the primary and the secondary focus of the ellipse, and its use in the study of analytical and numerical solutions of perturbed two-body problem. We take two approaches: first, the study of the analytical development of the basic quantities of the two-body problem to be used in the analytical theories of the planetary motion and second, the study of the minimization of the errors in the numerical integration by an appropriate choice of parameters in our family for each value of the eccentricity. The use of an appropriate value of the parameter can improve the length of the developments in the analytical theories and reduce the errors in the case of the numerical integration.

Numerical methods are usually required to solve the neutron diffusion equation applied to nuclear reactors due to its heterogeneous nature. The most popular numerical techniques are the Finite Difference Method (FDM), the Coarse Mesh Finite Difference Method (CFMD), the Nodal Expansion Method (NEM), and the Nodal Collocation Method (NCM), used virtually in all neutronic diffusion codes, which give accurate results in structured meshes. However, the application of these methods in unstructured meshes to deal with complex geometries is not straightforward and it may cause problems of stability and convergence of the solution. By contrast, the Finite Element Method (FEM) and the Finite Volume Method (FVM) are easily applied to unstructured meshes. On the one hand, the FEM can be accurate for smoothly varying functions. On the other hand, the FVM is typically used in the transport equations due to the conservation of the transported quantity within the volume. In this paper, the FVM algorithm implemented in the ARB Partial Differential Equations solver has been used to discretize the neutron diffusion equation to obtain the matrices of the generalized eigenvalue problem, which has been solved by means of the SLEPc library.

We discuss multigroup SIRS (susceptible, infectious, and recovered) epidemic models with random perturbations. We carry out a detailed analysis on the asymptotic behavior of the stochastic model; when reproduction number ${ℛ}_0>1$, we deduce the globally asymptotic stability of the endemic equilibrium by measuring the difference between the solution and the endemic equilibrium of the deterministic model in time average. Numerical methods are employed to illustrate the dynamic behavior of the model and simulate the system of equations developed. The effect of the rate of immunity loss on susceptible and recovered individuals is also analyzed in the deterministic model.