Results in Control and Optimization最新文献_第8页

The role of amensalism and parasitism on the dynamics of three species ecological system 寄生性和寄生性对三种生态系统动态的影响

Q3 Mathematics

Results in Control and Optimization

Pub Date : 2025-05-22 DOI: 10.1016/j.rico.2025.100571

Alyaa Raad Saleh Abd Alhadi, Raid Kamel Naji

This paper introduces a novel mathematical model of a three-species ecosystem that includes biological relationships such as amensalism and parasitism. Unlike most previous studies, it assumed that the ecosystem consists of three different kinds of interactions at the same time: two host–parasite interactions, while the third one is amensal–enemy interactions. To do the dynamic analysis of this system, all of the solution’s attributes were examined, and potential equilibrium points were found. The local stability was established using the linearization technique. The global stability was examined using Lyapunov functions. Every prerequisite for perseverance was identified. The effects of varying the parameters were investigated using the bifurcation theory. A computer simulation was applied to bolster our analytical research. It is observed that the proposed model has a globally stable coexistence point, while the periodic dynamics do not exist. The impact of amensalism and parasitism is clearly shown due to the transition of the solution from the coexistence point to the planar equilibrium points once their rates exceed a vital value, and conversely, it is proved that the system (3) undergoes a transcritical bifurcation near the first axial and the enemy–host-free equilibrium points.

本文介绍了一个新的三种生态系统的数学模型，其中包括寄生和寄生等生物关系。与之前的大多数研究不同，它假设生态系统同时由三种不同的相互作用组成：两种宿主-寄生虫相互作用，而第三种是天敌相互作用。为了对该系统进行动力学分析，检查了该系统的所有属性，并找到了潜在的平衡点。利用线性化技术建立了系统的局部稳定性。利用Lyapunov函数检验了系统的全局稳定性。坚持不懈的一切先决条件都已确定。利用分岔理论研究了参数变化的影响。计算机模拟被用来加强我们的分析研究。结果表明，该模型具有全局稳定共存点，而周期动力学不存在。一旦共存点和寄生点的速率超过临界值，解就从共存点过渡到平面平衡点，从而清楚地显示了寄生和寄生的影响，相反，证明了系统(3)在第一轴和无敌宿主平衡点附近经历了跨临界分岔。

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引用次数: 0

Addressing ORPD problem in a standard IEEE power network accompanied with RESs and FACTs appliances by COMMKE under volatile load scenarios comke在不稳定负载情况下解决带有RESs和FACTs设备的标准IEEE电网中的ORPD问题

Q3 Mathematics

Results in Control and Optimization

Pub Date : 2025-05-22 DOI: 10.1016/j.rico.2025.100572

Susanta Dutta , Tushnik Sarkar , Chandan Paul , Sabbir Reza Tarafdar , Provas Kumar Roy , Ghanshyam G. Tejani , Seyed Jalaleddin Mousavirad

This research examines the optimal reactive power dispatch (ORPD) problem across IEEE 30 & 118 bus experimental networks. In particular, we incorporate renewable energy sources (RESs) like solar photovoltaic (PV) and wind power (WP) into the conventional network after first balancing it. Both singular and multiple objective functions (OFs) are considered here. These are, both alone and together, a drop in aggregated voltage deviation (AVD) over buses and a reduction in active power loss (APL). Twenty one cases in all have been looked at using three test frameworks. TSC-TCR (FACTs devices) with test setup are being used for cases 4–6, 9–12 & 16–21. The objectives have been achieved by the use of the COMMKE algorithm, a multi-trial vector-based monkey king evolution (MMKE) method integrated with oppositional based learning (OBL) and chaotic based learning (CBL). Comparative analysis has also been done on the performance of the other optimization methods that were showcased in the latest ORPD research. Both constant and dynamic load demand scenarios are covered in the study. Appropriate probability density functions (PDF) are used to forecast the uncertain WP, PV source, and load demand. Uncertain situations with fluctuating load demand, wind speed (WS), and sun irradiation (SI) are simulated using Monte Carlo simulations (MCS). The investigations’ findings demonstrate that, in a variety of cases, the COMMKE outperforms optimization techniques found in the recent ORPD literature. The improvement of power network efficiency in ORPD difficulties by the application of TSC-TCR is another noteworthy conclusion. To scrutinize the performance of COMMKE, the identical experiments have been conducted using MMKE & driving training based optimization (DTB) and the results coming from COMMKE, MMKE & DTBO are compared. To make this comparison more lucid, statistical records are produced, box plots are presented, error bar plots are used and moreover one way ANOVA test has been performed over the results generated through the different optimization approaches.

本研究探讨IEEE 30 &；最优无功功率调度（ORPD）问题。118总线实验网络。特别是，我们将太阳能光伏（PV）和风能（WP）等可再生能源（RESs）纳入常规电网后，首先进行平衡。这里考虑了单目标函数和多目标函数。无论是单独还是一起，都可以降低总线上的聚合电压偏差（AVD），并降低有功功率损耗（APL）。总共有21个案例使用了三个测试框架。带有测试设置的TSC-TCR （FACTs器件）用于案例4 - 6,9 - 12 &；16日。该目标通过使用COMMKE算法实现，这是一种基于多试验向量的猴王进化（MMKE）方法，结合了基于对立学习（OBL）和基于混沌学习（CBL）。并对最新ORPD研究中所展示的其他优化方法的性能进行了对比分析。本研究涵盖了恒载和动载两种需求情况。采用适当的概率密度函数（PDF）来预测不确定的WP、PV源和负荷需求。采用蒙特卡罗模拟（MCS）方法对负荷需求、风速（WS）和太阳辐照（SI）波动的不确定情况进行了模拟。调查结果表明，在各种情况下，COMMKE优于最近ORPD文献中发现的优化技术。应用TSC-TCR提高ORPD困难地区电网效率是另一个值得注意的结论。为了检验COMMKE的性能，使用MMKE进行了相同的实验；基于驾驶训练的优化（DTB）以及来自COMMKE， MMKE和amp；对dbo进行比较。为了使这种比较更加清晰，产生了统计记录，呈现了箱形图，使用了误差柱图，并且对通过不同优化方法生成的结果进行了单向方差分析检验。

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引用次数: 0

Quantifying control measures for lumpy skin disease in cattle using a vector–host transmission model 用媒介-宿主传播模型定量控制牛肿块性皮肤病的措施

Q3 Mathematics

Results in Control and Optimization

Pub Date : 2025-05-21 DOI: 10.1016/j.rico.2025.100573

Din Prathumwan , Nattakarn Numpanviwat , Kamonchat Trachoo , Pearanat Chuchard , Inthira Chaiya

Purpose:

This study aims to develop a mathematical model to understand and control the spread of lumpy skin disease in cattle populations, incorporating blood-sucking insects as vectors.

Research Question:

How can the interaction between cattle and vectors be effectively modeled to assess the impact of control strategies such as quarantine and treatment on the transmission of lumpy skin disease?

Methodology:

The population dynamics are modeled using the SLIQR-SL framework, categorizing cattle into six disease states and vectors into two states. Stability analysis is performed to identify equilibrium points, and the basic reproduction number (

R_{0}

) is calculated to evaluate disease persistence or eradication conditions. Numerical simulations are conducted to assess various control strategies.

Validation:

The model’s predictions are validated through numerical examples, demonstrating its ability to replicate observed transmission patterns and evaluate control measures.

Results:

The analysis reveals that when

R_{0} < 1

, lumpy skin disease can be eradicated, but when

R_{0} > 1

, the disease persists. Numerical simulations highlight the critical role of quarantine and treatment in significantly reducing disease prevalence.

Significance:

The findings provide actionable insights for policymakers and veterinarians, emphasizing the importance of integrated control strategies in mitigating lumpy skin disease outbreaks and minimizing economic losses.

目的：以吸血昆虫为媒介，建立了解和控制牛块性皮肤病传播的数学模型。研究问题：如何有效地模拟牛与病媒之间的相互作用，以评估隔离和治疗等控制策略对结节性皮肤病传播的影响？方法：使用SLIQR-SL框架对种群动态进行建模，将牛分为六种疾病状态，将媒介分为两种状态。进行稳定性分析以确定平衡点，并计算基本繁殖数（R0）以评估疾病持续或根除条件。通过数值仿真来评估各种控制策略。验证：通过数值实例验证了模型的预测，证明了其复制观察到的传播模式和评估控制措施的能力。结果：分析发现，当R0>；1时，肿块性皮肤病可以根治，而当R0>；1时，肿块性皮肤病持续存在。数值模拟强调了隔离和治疗在显著降低疾病患病率方面的关键作用。意义：研究结果为决策者和兽医提供了可操作的见解，强调了综合控制策略在减轻结节性皮肤病暴发和减少经济损失方面的重要性。

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引用次数: 0

A new model of the impact of chronic hepatitis C and its treatment on the development of tuberculosis: An optimal control and sensitivity analysis 慢性丙型肝炎及其治疗对结核病发展影响的新模型：最优控制和敏感性分析

Q3 Mathematics

Results in Control and Optimization

Pub Date : 2025-05-19 DOI: 10.1016/j.rico.2025.100574

Chaimae El Mourabit, Nadia Idrissi Fatmi

This study offers a mathematical model with eight compartments that explain how tuberculosis spreads among individuals afflicted with HCV. The novelty of this work comes through mathematical modeling of the dynamics of tuberculosis in HCV cases on the one hand and in patients receiving DAA treatment on the other. We analyze the formulated model by proving a solution’s existence and showing the system solution’s positivity and boundedness. Furthermore, the model is reconstructed as an optimal control issue, considering three controls (consciousness, treatment, and early detection) to decrease the prevalence of tuberculosis in HCV-infected people, utilizing Pontryagin’s maximum principle. Finally, numerical simulations are performed using MATLAB, and the outcomes validate that treatment combined with early detection and consciousness reduces the spread of tuberculosis among individuals affected with HCV compared to scenarios without control, leading to improved overall outcomes.

这项研究提供了一个有8个区室的数学模型来解释结核病是如何在HCV患者中传播的。这项工作的新颖之处在于，一方面是通过对HCV病例和接受DAA治疗的患者的结核病动态进行数学建模。我们通过证明解的存在性和系统解的正性和有界性来分析模型。进一步，利用Pontryagin的最大值原理，将模型重构为一个最优控制问题，考虑意识、治疗和早期发现三个控制因素，以降低hcv感染者的结核病患病率。最后，使用MATLAB进行数值模拟，结果验证了与不加控制的情况相比，治疗结合早期发现和意识减少了HCV患者中结核病的传播，从而改善了总体结果。

引用次数: 0

Opinion mining in e-commerce: Evaluating machine learning approaches for sentiment analysis 电子商务中的意见挖掘：评估情感分析的机器学习方法

Q3 Mathematics

Results in Control and Optimization

Pub Date : 2025-05-18 DOI: 10.1016/j.rico.2025.100575

L. Lakshmi , Ali B.M. Ali , K Dhana Sree Devi , Muhammad Rafiq , Iskandar Shernazarov , Nashwan Adnan Othman , M. Ijaz Khan

In recent years, opinion mining has played a major role in analyzing text data from various sources such as Amazon, Capterra, Facebook, Google, GetApp, and Twitter. It enables companies to actively refine their business strategies. Sentiment analysis involves interpreting and classifying customer emotions (positive, neutral, and negative) expressed in reviews using sentiment analysis techniques such as BING and AFINN. This paper presents four approaches for customer review analysis and classification: the grade-based approach, content-based approach, content-based NRC-Emotion Lexicon approach, and collaborative approach. We employ three machine learning algorithms—stacking, random forest, and LogitBoost—to evaluate the performance of these approaches. A real-time dataset from Amazon product reviews is used for training and testing the model. Empirical results reveal that the collaborative approach outperforms the grade-based, content-based, and content-based NRC-Emotion Lexicon approaches across all three machine learning algorithms. Additionally, all approaches demonstrate outstanding performance when using the boosting algorithm for customer review classification.

近年来，意见挖掘在分析来自亚马逊、Capterra、Facebook、b谷歌、GetApp和Twitter等各种来源的文本数据方面发挥了重要作用。它使公司能够积极地改进他们的商业战略。情感分析涉及使用情感分析技术（如BING和AFINN）对评论中表达的客户情绪（积极、中立和消极）进行解释和分类。本文提出了四种客户评论分析和分类方法：基于分数的方法、基于内容的方法、基于内容的NRC-Emotion Lexicon方法和协作方法。我们使用了三种机器学习算法——堆叠、随机森林和logitboost——来评估这些方法的性能。来自亚马逊产品评论的实时数据集用于训练和测试模型。实证结果表明，协作方法在所有三种机器学习算法中都优于基于成绩、基于内容和基于内容的NRC-Emotion Lexicon方法。此外，在使用提升算法进行客户评论分类时，所有方法都表现出出色的性能。

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引用次数: 0

Localization of partial discharge in the high voltage apparatus 高压设备局部放电的定位

Q3 Mathematics

Results in Control and Optimization

Pub Date : 2025-05-03 DOI: 10.1016/j.rico.2025.100562

Amir Ghaedi , Mehrdad Mahmoudian , Eduardo M.G. Rodrigues , Rui Melicio

Partial discharges (PD) in high-voltage (HV) devices can be used as indicators of insulation deterioration, often preceding catastrophic failures in power systems. This paper presents a novel approach for locating and identifying PD sources in HV equipment, targeting insulation condition monitoring in power transformers, XLPE cables, and generators. The new technique utilizes the correlation between PD signal energy characteristics to estimate the source location. The effectiveness of the proposed method is validated through selected case studies involving XLPE cables, transformers, and generators. The results demonstrate that the technique can accurately locate PD sources, potentially enhancing the reliability and longevity of HV power equipment. Key contributions of this work include: a comprehensive review of PD detection sensors, with a focus on electrical methods for high-frequency pulse measurement; experimental characterization of PD signals in XLPE cables and transformers, providing insights into their frequency properties; development of a correlation-based algorithm for PD localization, utilizing a database of simulated PD signals; and validation of the proposed method through EMTP-RV simulations and MATLAB signal processing, showing high accuracy in PD source localization. However, the proposed technique has limitations that prevents its generalized which are highlighted in the paper.

高压（HV）设备的局部放电（PD）可以作为绝缘劣化的指标，通常在电力系统发生灾难性故障之前发生。本文提出了一种定位和识别高压设备中局部放电源的新方法，用于电力变压器、交联聚乙烯电缆和发电机的绝缘状态监测。该方法利用PD信号能量特性之间的相关性来估计源位置。通过对XLPE电缆、变压器和发电机的案例研究，验证了所提出方法的有效性。结果表明，该技术可以准确定位局部放电源，有可能提高高压电力设备的可靠性和寿命。这项工作的主要贡献包括：PD检测传感器的全面回顾，重点是高频脉冲测量的电气方法；XLPE电缆和变压器中PD信号的实验表征，提供对其频率特性的见解；利用模拟PD信号的数据库，开发了一种基于相关性的PD定位算法；并通过EMTP-RV仿真和MATLAB信号处理验证了该方法的有效性，表明该方法具有较高的PD源定位精度。然而，所提出的技术有局限性，阻碍了它的推广，这是本文强调的。

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引用次数: 0

Bayesian topology inference of regulatory networks under partial observability 部分可观测条件下调控网络的贝叶斯拓扑推断

Q3 Mathematics

Results in Control and Optimization

Pub Date : 2025-05-01 DOI: 10.1016/j.rico.2025.100570

Mohammad Alali, Mahdi Imani

Biological systems, such as microbial communities in metagenomics and gene regulatory networks (GRNs) in genomics, are composed of a vast number of interacting components observed through inherently noisy data. These systems play a critical role in understanding fundamental biological processes, including gene regulation, microbial interactions, and cellular dynamics. For example, microbial communities involve complex interactions between microbes, bacteria, genes, and small molecules observed through omics data, while GRNs consist of numerous interacting genes observed via various gene-expression technologies. However, reconstructing the topology of such networks poses significant challenges due to their large scale, high dimensionality, and the presence of noise. Existing inference techniques often struggle with scalability, interpretability, and overfitting, making them unsuitable for analyzing large and complex biological systems. To overcome these challenges, this paper proposes a Bayesian topology optimization framework for efficient and scalable inference of regulatory networks modeled as partially-observed Boolean dynamical systems (POBDS). The method combines the Boolean Kalman Filter (BKF) as an optimal estimator for POBDS, with Bayesian optimization, which employs Gaussian Process regression and a topology-inspired kernel function to model the log-likelihood function. Numerical experiments demonstrate the superior performance of our framework. In the p53-MDM2 network, our method accurately infers topology with 8 and 16 unknown regulations, achieving higher log-likelihood with 100 and 200 evaluations, respectively. For the mammalian cell cycle network with 10 unknown regulations, proposed method identifies the correct topology among 59,049 possibilities with lower error and faster convergence.

生物系统，如宏基因组学中的微生物群落和基因组学中的基因调控网络（grn），由大量通过固有噪声数据观察到的相互作用成分组成。这些系统在理解基本的生物过程中起着关键作用，包括基因调控、微生物相互作用和细胞动力学。例如，微生物群落涉及微生物、细菌、基因和通过组学数据观察到的小分子之间复杂的相互作用，而grn由通过各种基因表达技术观察到的众多相互作用基因组成。然而，由于这些网络的大规模、高维和存在噪声，重建这些网络的拓扑结构面临着重大挑战。现有的推理技术经常与可扩展性、可解释性和过拟合作斗争，使它们不适合分析大型和复杂的生物系统。为了克服这些挑战，本文提出了一个贝叶斯拓扑优化框架，用于部分观测布尔动力系统（POBDS）模型的有效和可扩展的调节网络推理。该方法将布尔卡尔曼滤波（BKF）作为POBDS的最优估计器，与贝叶斯优化相结合，采用高斯过程回归和拓扑启发核函数对对数似然函数进行建模。数值实验证明了该框架的优越性能。在p53-MDM2网络中，我们的方法准确地推断出具有8个和16个未知规则的拓扑，分别获得了100次和200次评估的更高的对数似然。对于含有10个未知规则的哺乳动物细胞周期网络，该方法在59049种可能性中识别出正确的拓扑结构，误差更小，收敛速度更快。

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引用次数: 0

Fuzzy PD control for a quadrotor with experimental results 四旋翼飞行器的模糊PD控制及实验结果

Q3 Mathematics

Results in Control and Optimization

Pub Date : 2025-04-30 DOI: 10.1016/j.rico.2025.100568

Anh T. Nguyen , Nam H. Nguyen , Mien L. Trinh

Quadrotor is an unmanned aerial vehicle widely used in traffic construction monitoring, volcano monitoring, forest fire, power line inspection, missing person search and disaster relief. The dynamic model of quadrotor becomes complex and non-linear due to four motors with four propellers to control and stabilize the motion. One disadvantage of the traditional PID controller is that its parameters are tuned based on trials and errors, but the fuzzy PID controller will automatically adjust its PID gains based on the IF-THEN rules and the parameters of the fuzzy systems are designed beforehand. For other adaptive fuzzy controllers, their parameters are online updated with large computational load. In this paper, we design an intelligent controller to manage the operating state of quadrotor (UAV) by combining the advantages of traditional PD controller with fuzzy logic inference systems to tune its parameters. These Fuzzy PD controllers performs control of the movement of the quadrotor along three axes to follow the desired trajectory. The proposed Fuzzy PD control system for the quadrotor is simulated and evaluated on Matlab-Simulink, then conducted with real-time experiments on QDrone2 physical system. Simulation and experimental results with comparisons to the PD controller have proven the effectiveness of the proposed control method with small tracking error under the impact of time-varying disturbance and additional load.

四旋翼无人机是一种广泛应用于交通建设监控、火山监测、森林火灾、电力线检查、失踪人员搜索和救灾等领域的无人机。四旋翼飞行器由于有四个电机和四个螺旋桨来控制和稳定运动，使其动力学模型变得复杂和非线性。传统PID控制器的一个缺点是其参数是基于试错调整的，而模糊PID控制器会根据IF-THEN规则自动调整PID增益，并且模糊系统的参数是事先设计好的。其他自适应模糊控制器的参数在线更新，计算量大。本文结合传统PD控制器和模糊逻辑推理系统的优点，设计了一种四旋翼无人机（UAV）运行状态的智能控制器。这些模糊PD控制器执行沿三轴四旋翼的运动控制，以遵循所需的轨迹。在Matlab-Simulink中对所提出的四旋翼模糊PD控制系统进行了仿真和评估，并在QDrone2物理系统上进行了实时实验。仿真和实验结果表明，该控制方法在时变扰动和附加负载的影响下具有较小的跟踪误差。

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引用次数: 0

Practical implementation of a type-2 fuzzy logic controller for steering a service robot 服务机器人控制的2型模糊控制器的实际实现

Q3 Mathematics

Results in Control and Optimization

Pub Date : 2025-04-28 DOI: 10.1016/j.rico.2025.100558

Suci Dwijayanti, Bhakti Y. Suprapto, Ichlasul A. Rizky

Service robots are designed to assist humans in various tasks and often rely on wheeled locomotion for navigation. Effective robot movement requires a robust control system to regulate steering and ensure precise maneuvering toward locations. However, a common challenge in service robot navigation is the lack of precision in steering control. To address this issue, this study implements and evaluates a steering control system for wheeled service robots using a type-2 fuzzy logic controller (T2-FLC). The proposed T2-FLC system incorporates two input variables: error (difference between the setpoint determined by the light detection and ranging sensor and the steering encoder reading) and de-error (difference between the current and previous error values). Subsequently, these inputs are converted into three, five, or seven membership functions (MFs). Comparative simulation analysis revealed that the T2-FLC with seven MFs outperformed that with alternative MF configurations and a conventional type-1 FLC and achieved a minimal steady-state error of 0.0118. Real-time experiments further validated these findings, with the seven-MF T2-FLC producing a steady-state error of only 3.6 during a 90° setpoint test. In obstacle navigation trials, a T2-FLC-equipped robot navigated to target destinations in 32.49 s in stationary obstacle scenarios and within 41.78 s in dynamic obstacle environments. These findings confirm that the T2-FLC significantly enhances steering performance, making it viable for controlling service robot navigation.

服务机器人是为协助人类完成各种任务而设计的，通常依靠轮式运动进行导航。有效的机器人运动需要一个强大的控制系统来调节转向，并确保精确的机动到位置。然而，服务机器人导航面临的一个共同挑战是转向控制的精度不足。为了解决这一问题，本研究利用2型模糊逻辑控制器（T2-FLC）实现并评估了轮式服务机器人的转向控制系统。所提出的T2-FLC系统包含两个输入变量：误差（由光检测和测距传感器确定的设定值与转向编码器读数之间的差异）和去误差（当前和以前的误差值之间的差异）。随后，这些输入被转换为三个、五个或七个隶属函数（mf）。对比仿真分析表明，具有7个MF的T2-FLC优于其他MF配置和传统1型FLC，稳态误差最小为0.0118。实时实验进一步验证了这些发现，在90°设定值测试中，7 - mf T2-FLC产生的稳态误差仅为3.6。在障碍物导航试验中，配备t2 - flc的机器人在静止障碍物场景下导航到目标目的地的时间为32.49 s，在动态障碍物环境下导航到目标目的地的时间为41.78 s。这些研究结果证实，T2-FLC显著提高了转向性能，使其成为控制服务机器人导航的可行方法。

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引用次数: 0

Effect of fear in a fractional order prey–predator model with time delayed carrying capacity 具有时间延迟承载能力的分数阶捕食模型中恐惧的影响

Q3 Mathematics

Results in Control and Optimization

Pub Date : 2025-04-25 DOI: 10.1016/j.rico.2025.100567

Pramodh Bharati , Subrata Paul , Animesh Mahata , Supriya Mukherjee , Subhabrata Mondal , Banamali Roy

The Caputo technique is used in this article to analyze the fractional-order predator–prey scenario. Incorporating a delayed carrying capacity for the prey population and posing the impact of individual prey fear on predators are two aspects of this. We first provide the model’s formulation in terms of an integer order derivative, and subsequently we expand it to a fractional order system in terms of the Caputo derivative. The article contains a number of conclusions about the prerequisites for the model’s existence and uniqueness as well as the restrictions on the boundedness and positivity of the solution. To satisfy the requirements for the existence and uniqueness of the precise solution, the Lipschitz condition is applied. Within the local context, we have examined the stability of equilibrium points. Additionally, we investigated whether Hopf bifurcation may occur at the interior equilibrium point of our suggested model. We have used the Generalised Euler technique to approximatively solve the model. The suggested scheme’s dependability is indicated by the fact that the results produced using the current numerical approach converge to equilibrium for the fractional order. For our research, MATLAB was used to enable graphical representations and numerical simulations.

本文使用Caputo技术来分析分数阶捕食者-猎物场景。将猎物种群的延迟承载能力与单个猎物对捕食者的恐惧的影响结合起来是这方面的两个方面。我们首先提供了一个整数阶导数的模型公式，随后我们将其扩展到一个分数阶系统的Caputo导数。本文给出了模型存在唯一性的先决条件以及解的有界性和正性的限制条件。为了满足精确解的存在唯一性要求，应用了Lipschitz条件。在局部情况下，我们考察了平衡点的稳定性。此外，我们还研究了Hopf分岔是否可能发生在我们建议的模型的内部平衡点上。我们使用广义欧拉技术对模型进行了近似求解。采用现有数值方法得到的结果收敛于分数阶的平衡态，表明了所提方案的可靠性。在我们的研究中，使用MATLAB进行图形表示和数值模拟。

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引用次数: 0