Journal of Applied Mathematics and Computing最新文献

This study explores a prey-predator model with a Holling type II functional response, focusing on how predation-induced fear affects prey dynamics. Assuming a decline in prey population growth rate attributed to predator-induced fear, the model incorporates a fear response delay representing prey detection time, along with gestation delay. The system’s positivity, boundedness, and permanence are proved under certain parametric conditions. The local stability is discussed at trivial, semi-trivial, and positive equilibria. The system exhibits Hopf bifurcation with respect to both delays. Hopf bifurcation analysis is done for different combinations of delays. Furthermore, the properties of periodic solutions in the delayed system are also determined. An extensive numerical simulation has been performed to validate analytical findings. The occurrence of Hopf bifurcation is shown for different combinations of delays by plotting eigenvalues.

Combined oncolytic virotherapy and immunotherapy are novel treatment protocols that represent a promising and advantageous strategy for various cancers, surpassing conventional anti-cancer treatments. This is due to the reduced toxicity associated with traditional cancer therapies. We present a mathematical model that describes the interactions between tumor cells, the immune response, and the combined application of virotherapy and interleukin-2 (IL-2). A stability analysis of the model for both the tumor and tumor-free states is discussed. To gain insight into the impact of model parameters on tumor cell growth and inhibition, we perform a sensitivity analysis using Latin hypercube sampling to compute partial rank correlation coefficient values and their associated p-values. Furthermore, we perform optimal control techniques using the Pontryagin maximum principle to minimize tumor burden and determine the most effective protocol for the administered treatment. We numerically demonstrate the ability of combined virotherapy and IL-2 to eliminate tumors.

The fourth industrial revolution, in which mechanical appliances can be precisely and automatically handled, depends extensively on intelligent manufacturing. It has the potential to create more productive manufacturing facilities. Still, defects and possible mishaps in the production process affect the workflow, deplete resources, and worsen environmental effects. Failure modes and effects analysis (FMEA) is a systematic method for identifying, analyzing, and removing possible failures in products, designs, and procedures. Due to uncertainty’s multiple nature, more than one method or technique is needed to deal with such flaws or failures. Ultimately, there is a dire need to develop hybrid models to address and resolve manufacturing process failures. Many fuzzy rough MCDM techniques have been designed to deal with and quantify uncertainty when assessing failure modes; these methods often use triangular fuzzy numbers and FMEA. When modeling complex and asymmetric fuzzy sets, trapezoidal fuzzy numbers offer a more expressive and accurate alternative to the more basic and limited triangle fuzzy numbers. This study proposes a novel approach to prioritize FMEA risks by combining trapezoidal fuzzy rough numbers with VIKOR method to address ambiguity in expert opinions. Using fuzzy rough intervals rather than a single crisp value, fuzzy rough numbers are utilized to deal with ambiguous information regarding linguistic variables. Robots employed in the cabal industry can have their potential failures identified and assessed more effectively with the help of the suggested trapezoidal fuzzy rough FMEA technique.

In recent years, there has been a notable increase in atmospheric carbon dioxide ((hbox {CO}_2)) levels, primarily due to the burning of fossil fuels, which has led to heightened global warming and negative repercussions for human populations. As a result, governments are striving to diminish reliance on fossil fuels by promoting the adoption of renewable energy sources. This research introduces a nonlinear mathematical model that has been developed to examine the consequences of shifting the population from traditional energy sources, such as coal, oil, and gas to renewable alternatives like solar, wind, and hydropower. The concept revolves around governments encouraging the adoption of renewable energy by the public as (hbox {CO}_2) levels increase, thereby enabling a phased transition away from conventional energy sources. The population is divided into two segments: those dependent on conventional energy and those opting for green alternatives due to their understanding of the environmental impact of fossil fuels and (hbox {CO}_2) emission. Our analysis suggests that if the demand for energy from traditional sources surpasses a certain threshold, atmospheric (hbox {CO}_2) levels may begin to fluctuate periodically. To maintain (hbox {CO}_2) concentrations at a lower level, there must be a significant rate of transition from traditional to renewable energy sources within the population.

This paper studies several types of robust control cycles (RCCs) for the Boolean control networks (BCNs) affected by disturbances using semi-tensor product of matrices, and provides their computing methods. First, the cycles of a BCN are classified as strong RCCs and weak RCCs according to their ability to resist disturbances. Secondly, the properties of the states on a cycle for the BCNs are revealed, based on which all the RCCs whose weak connecting degree is not more than one with certain length are obtained. Moreover, the controls to ensure that the state trajectories form RCCs are designed. Finally, some examples are given to demonstrate the effectiveness of the obtained theoretical results, as well as to show the applications of these results.

Malaria, a lethal protozoan disease transmitted through the bites of female Anopheles mosquitoes infected with Plasmodium parasites, remains a significant global health concern. This study introduces a compartmental mathematical model to explore the impact of insecticide use and malaria treatment based on awareness initiatives. The model incorporates the influence of media-based awareness on the effectiveness of insecticide utilization for malaria control. Key mathematical properties, such as positivity, boundedness of solutions, feasibility, and stability of equilibria, are systematically investigated. Our analysis demonstrates that all solutions to the system are positive and bounded within a specified set of initial conditions, establishing the mathematical soundness and epidemiological relevance of the model. The basic reproduction number (R_0) is determined through the next-generation matrix method. Stability analysis reveals that the disease-free equilibrium is globally asymptotically stable when (R_0) is less than one, while it becomes unstable if (R_0) exceeds one. Global stability of the endemic equilibrium is established using an appropriate quadratic Lyapunov function in cases where (R_0) surpasses one. We identify the most sensitive parameters of the model through normalized forward sensitivity indices. In addition, numerical simulations employing the Runge–Kutta method in Python software further validate our findings. Both analytical and numerical results collectively suggest that the integration of awareness-based insecticide usage with malaria treatment holds the potential for malaria elimination. This comprehensive approach not only contributes to the mathematical rigor of the model but also underscores its practical implications for effective malaria control strategies.

Maximum distance separable (MDS) matrices play a crucial role not only in coding theory but also in the design of block ciphers and hash functions. Of particular interest are involutory MDS matrices, which facilitate the use of a single circuit for both encryption and decryption in hardware implementations. In this article, we present several characterizations of involutory MDS matrices of even order. Additionally, we introduce a new matrix form for obtaining all involutory MDS matrices of even order and compare it with other matrix forms available in the literature. We then propose a technique to systematically construct all (4 times 4) involutory MDS matrices over a finite field (mathbb {F}_{2^m}). This method significantly reduces the search space by focusing on involutory MDS class representative matrices, leading to the generation of all such matrices within a substantially smaller set compared to considering all (4 times 4) involutory matrices. Specifically, our approach involves searching for these representative matrices within a set of cardinality ((2^m-1)^5). Through this method, we provide an explicit enumeration of the total number of (4 times 4) involutory MDS matrices over (mathbb {F}_{2^m}) for (m=3,4,ldots ,8).

A single machine scheduling problem takes into account a common due window assignment, including delivery time, resource allocation and learning effect. The basic processing time, position and allotted resources are all linked to the actual processing time. We take into consideration three goal functions, which minimize the costs of earliness, tardiness, start time of window, window size, resource allocation and makespan. The aim is to find the optimal sequence and distribution of resources. Polynomial time algorithms are provided for each of the three issues. The algorithms have (O(n^3)) levels of complexity, where n is the number of jobs. Special cases with the same learning rates are also considered. Polynomial time algorithms are also provided for each of the special cases. The algorithms have (O(ntextrm{log}n)) levels of complexity.

Rapidly developing machine learning methods have stimulated research interest in computationally reconstructing differential equations (DEs) from observational data, providing insight into the underlying mechanistic models. In this paper, we propose a new neural-ODE-based method that spectrally expands the spatial dependence of solutions to learn the spatiotemporal DEs they obey. Our spectral spatiotemporal DE learning method has the advantage of not explicitly relying on spatial discretization (e.g., meshes or grids), thus allowing reconstruction of DEs that may be defined on unbounded spatial domains and that may contain long-ranged, nonlocal spatial interactions. By combining spectral methods with the neural ODE framework, our proposed spectral DE method addresses the inverse-type problem of reconstructing spatiotemporal equations in unbounded domains. Even for bounded domain problems, our spectral approach is as accurate as some of the latest machine learning approaches for learning or numerically solving partial differential equations (PDEs). By developing a spectral framework for reconstructing both PDEs and partial integro-differential equations (PIDEs), we extend dynamical reconstruction approaches to a wider range of problems, including those in unbounded domains.

This work emphasizes the computational and analytical analysis of integral-differential equations, with a particular application in modeling avoidance learning processes. Firstly, we suggest an approach to determine a unique solution to the given model by employing methods from functional analysis and fixed-point theory. We obtain numerical solutions using the approach of Picard iteration and evaluate their stability in the context of minor perturbations. In addition, we explore the practical application of these techniques by providing two examples that highlight the thorough analysis of behavioral responses using numerical approximations. In the end, we examine the efficacy of our suggested ordinary differential equations (ODEs) for studying the avoidance learning behavior of animals. Furthermore, we investigate the convergence and error analysis of the proposed ODEs using multiple numerical techniques. This integration of theoretical and practical analysis enhances the domain of applied mathematics by providing important insights for behavioral science research.