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Analysis of the hate speech and racism co-existence dissemination model with optimal control strategies 用最优控制策略分析仇恨言论与种族主义共存的传播模式
Q1 Mathematics Pub Date : 2024-04-23 DOI: 10.1016/j.csfx.2024.100109
Shewafera Wondimagegnhu Teklu, Yohannes Fissha Abebaw

Hate speech, racism, and their co-existence are the human mind infections that are major factors that affect the living conditions of people, societal well-being, and political stability, economic and social disturbance throughout the world especially in underdeveloped nations of the world. The main objective of this study is to formulate and analyze the hate-speech and racism co-existence model with optimal control strategies and investigate the optimal effects of protection and improvement (rehabilitation) strategies to minimize and tackle the hate speech and racism co-existence dissemination in the community. In this study, we have computed the hate speech sub-model, the racism sub-model, and the hate speech and racism co-existence model equilibrium points and analyzed their stabilities, using the next generation operator approach all the models' effective reproduction numbers are computed, examined the phenomenon of backward bifurcation whenever the model effective reproduction number is less than one where at which both the positive co-existence free equilibrium point and the positive co-existence dominance equilibrium point exist simultaneously. To achieve the objective minimizing the hate speech and racism co-existence dissemination dynamics by implementing the efforts towards the protection and improvement (rehabilitation) strategies, the optimal control problem is re-formulated, and optimal control analysis is performed for the co-existence model using Pontryagin's maximum principle. Numerical simulations using MATLAB ode45 solver with fourth-order Runge-Kutta numerical methods to investigate the behavior of the co-existence model solutions and to explore the optimal effects of the protections and improvements (rehabilitation) strategies for the hate speech and racism co-existence dynamics are then performed. From the results, we observed that implementing the protection and improvement (rehabilitation) strategies simultaneously is the most effective approach to minimize and tackle the speech and racism co-existence propagation in the community.

仇恨言论、种族主义及其共存是人类心灵的传染病,是影响全世界尤其是世界欠发达国家人民生活条件、社会福祉、政治稳定、经济和社会动荡的主要因素。本研究的主要目的是制定和分析具有最优控制策略的仇恨言论与种族主义共存模型,并研究保护和改善(康复)策略的最佳效果,以最大限度地减少和解决仇恨言论与种族主义共存在社区中的传播。在本研究中,我们计算了仇恨言论子模型、种族主义子模型以及仇恨言论与种族主义共存模型的均衡点,并分析了它们的稳定性,利用下一代算子方法计算了所有模型的有效繁殖数,考察了当模型有效繁殖数小于1时的向后分叉现象,在该现象中,正共存自由均衡点和正共存支配均衡点同时存在。为了实现通过实施保护和改善(康复)战略将仇恨言论和种族主义共存传播动态最小化的目标,对最优控制问题进行了重新表述,并利用庞特里亚金最大原则对共存模型进行了最优控制分析。然后,利用 MATLAB ode45 求解器和四阶 Runge-Kutta 数值方法进行了数值模拟,以研究共存模型解的行为,并探讨保护和改进(康复)策略对仇恨言论和种族主义共存动态的最佳影响。结果表明,同时实施保护和改善(恢复)策略是最小化和解决社区中言论和种族主义共存传播的最有效方法。
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引用次数: 0
An investigation into the controllability of multivalued stochastic fractional differential inclusions 多值随机分数微分夹杂的可控性研究
Q1 Mathematics Pub Date : 2024-02-19 DOI: 10.1016/j.csfx.2024.100107
Pallavi Bedi , Anoop Kumar , Gaurav Deora , Aziz Khan , Thabet Abdeljawad

This research aims to investigate the approximate controllability of multivalued impulsive stochastic fractional differential inclusions in Hilbert space with ABC fractional-order derivatives. First, we confirm the existence of mild solutions for the proposed control system using stochastic analysis, resolvent operator theory, and the fixed point technique. Secondly, we discuss a new set of sufficient conditions for the approximate controllability of the systems. The results are obtained under the assumption that the associated linear system is approximately controllable. Finally, an example is provided to illustrate the obtained results.

本研究旨在探讨具有 ABC 分数阶导数的希尔伯特空间多值脉冲随机分数微分夹杂的近似可控性。首先,我们利用随机分析、解析算子理论和定点技术证实了所提控制系统存在温和解。其次,我们讨论了系统近似可控性的一组新的充分条件。这些结果是在相关线性系统近似可控的假设条件下获得的。最后,我们提供了一个例子来说明所获得的结果。
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引用次数: 0
Moment dynamics for stochastic resonance in active rotator systems 主动转子系统中随机共振的力矩动力学
Q1 Mathematics Pub Date : 2024-02-15 DOI: 10.1016/j.csfx.2024.100108
Ruonan Liu , Yanmei Kang

We investigate the dynamics of active rotator systems by the moment closure method based on matching derivatives. This method is illustrated and verified in terms of three systems: the single-element rotator, the two coupled rotators and the mean field coupled rotators. Using the moment closure method, we study the effect of common noise on active rotator systems from the perspective of stochastic resonance. It is shown that the noise-induced stochastic resonance and parameter-induced stochastic resonance occur in the above three systems. Our observation discloses that the two kinds of stochastic resonance effect can be enhanced by both increasing coupling strength and the number of coupled rotators.

我们用基于匹配导数的力矩闭合法研究了有源转子系统的动力学。该方法在三个系统中进行了说明和验证:单元素旋转器、两个耦合旋转器和平均场耦合旋转器。利用矩闭合方法,我们从随机共振的角度研究了普通噪声对有源转子系统的影响。结果表明,在上述三个系统中出现了噪声诱导的随机共振和参数诱导的随机共振。我们的观察结果表明,通过增加耦合强度和耦合转子的数量,可以增强这两种随机共振效应。
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引用次数: 0
Stability, numerical simulations, and applications of Helmholtz-Duffing fractional differential equations 赫尔姆霍兹-杜芬分数微分方程的稳定性、数值模拟和应用
Q1 Mathematics Pub Date : 2024-02-08 DOI: 10.1016/j.csfx.2024.100106
M. Sivashankar , S. Sabarinathan , Kottakkaran Sooppy Nisar , C. Ravichandran , B.V. Senthil Kumar

The Helmholtz-Duffing equation with the Caputo fractional order derivative will be introduced in this article. We employ the fixed point theory to establish the existence and uniqueness results and prove the Hyers-Ulam stability. Drone applications for controlling the synthesis of external forces in torque, angular velocity, and projection served as a source of motivation. In the end, we developed numerical simulations to support our theoretical findings.

本文将介绍具有 Caputo 分数阶导数的 Helmholtz-Duffing 方程。我们利用定点理论建立了存在性和唯一性结果,并证明了 Hyers-Ulam 稳定性。无人机在扭矩、角速度和投影等外力合成控制方面的应用是研究的动力来源。最后,我们进行了数值模拟,以支持我们的理论发现。
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引用次数: 0
Stability analysis and suppress chaos in the generalized Lorenz model 广义洛伦兹模型的稳定性分析与混沌抑制
Q1 Mathematics Pub Date : 2024-02-07 DOI: 10.1016/j.csfx.2024.100104
Hamza Rouah

In this paper, we investigate the stability analysis of the equilibrium points and the influence of the orientation on the suppression of chaotic behavior of the generalized Lorenz system proposed. A three-dimensional system model is obtained using the spectral method. We proved that the first equilibrium point is globally asymptotically stable and the other two equilibria are asymptotically stable under certain conditions on the control parameters σ, P, r, b1 and b2. These theoretical results are supported by numerical simulations. Also, we showed that chaos can be suppressed by a boundary crisis or period-doubling by choosing an appropriate tilt angle. Bifurcation diagrams are drawn to confirm these results.

本文研究了所提出的广义洛伦兹系统平衡点的稳定性分析以及取向对抑制混沌行为的影响。利用谱法得到了一个三维系统模型。我们证明了在控制参数 σ、P、r、b1 和 b2 的特定条件下,第一个平衡点是全局渐近稳定的,另外两个平衡点也是渐近稳定的。这些理论结果得到了数值模拟的支持。此外,我们还表明,通过选择适当的倾斜角,可以用边界危机或周期加倍来抑制混沌。我们绘制了分岔图来证实这些结果。
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引用次数: 0
Parameters estimation, global sensitivity analysis and model fitting for the dynamics of Plutella xylostella infestations in a cabbage biomass 甘蓝生物量中木虱侵染动态的参数估计、全局敏感性分析和模型拟合
Q1 Mathematics Pub Date : 2024-01-30 DOI: 10.1016/j.csfx.2024.100105
Daniel Paul , Maranya Makuru Mayengo , Salamida Daudi

Plutella xylostella, commonly called Diamondback moth (DBM), a highly destructive and rapidly spreading agricultural pest originally from Europe. This pest poses a significant threat to global food security, with estimates suggesting that periodic outbreaks of Diamondback moth lead to annual crop losses of up to $US 45 billion worldwide. Given the potential for such substantial losses, it is crucial to employ various methods and techniques to understand the factors affecting the interaction between Diamondback moths and cabbage plants, which, in turn, impact cabbage biomass. In this paper, we propose a deterministic ecological model to capture the dynamics of Plutella xylostella infestations in cabbage biomass. The model is designed based on the life cycle stages of the pest, aiming at targeting the specific stage effectively. The synthetic data is generated using Least Square Algorithm through addition of Gaussian noise into numerically obtained values from existing literature to simulate real-world data. Global sensitivity analysis was done through Latin Hypercube sampling, highlights the significance of parameters such as ψ,αE and δ positively influence the growth of the diamondback moth in a cabbage biomass. In light of these findings, the study proposes that control strategies should be specifically directed towards these sensitive parameters. By doing so, we mitigate the pest population and enhance cabbage production.

木虱(Plutella xylostella)俗称钻心虫(DBM),原产于欧洲,是一种破坏性极强、传播迅速的农业害虫。这种害虫对全球粮食安全构成重大威胁,据估计,金刚夜蛾的周期性爆发导致全球每年农作物损失高达 40 亿至 50 亿美元。鉴于可能造成如此巨大的损失,采用各种方法和技术来了解影响金刚夜蛾与卷心菜植物之间相互作用的因素,进而影响卷心菜的生物量至关重要。在本文中,我们提出了一个确定性生态模型,以捕捉小菜蛾在小白菜生物量中的侵染动态。该模型是根据害虫的生命周期阶段设计的,旨在有效地针对特定阶段进行防治。合成数据采用最小平方算法生成,通过在现有文献的数值中加入高斯噪声来模拟现实世界的数据。通过拉丁超立方取样进行了全局敏感性分析,结果表明ψ、αE 和 δ 等参数的重要性对卷心菜生物量中钻心虫的生长有积极影响。鉴于这些发现,本研究建议应专门针对这些敏感参数采取控制策略。这样做既能减少害虫数量,又能提高甘蓝产量。
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引用次数: 0
A new method for a semi-positone Hadamard fractional boundary value problem 半正数Hadamard分数边值问题的一种新方法
Q1 Mathematics Pub Date : 2023-12-05 DOI: 10.1016/j.csfx.2023.100102
Rui Liu , Chengbo Zhai , Jing Ren

A Hadamard fractional boundary value problem with semi-positone nonlinearity is studied in this paper, and the local existence and uniqueness of solutions are derived by a recent fixed point theorem involving with increasing φ(h,r)-concave operators defined on ordered spaces. This is an unprecedented approach to solve the semi-positone problems. In practice, this method has a wider range of applicability since it can obtain the local uniqueness of the solutions. Furthermore, we can approximate the unique solution by constructing convergent iterative sequences. In the end, a persuasive example is provided to illustrate that the theoretical results we obtained are applicable and valid.

研究了一类半正负非线性的Hadamard分数阶边值问题,利用一个新的不动点定理,得到了该问题解的局部存在唯一性,该不动点定理涉及在有序空间上定义的φ−(h,r)-凹算子的递增。这是一种前所未有的解决半正极问题的方法。在实际应用中,该方法可以获得解的局部唯一性,适用范围更广。此外,我们可以通过构造收敛迭代序列来逼近唯一解。最后,通过一个有说服力的实例说明了所得理论结果的适用性和有效性。
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引用次数: 0
Asymptotics for peakon-antipeakon collision in a general Camassa-Holm model 一般Camassa-Holm模型中peakon反尖峰碰撞的渐近性
Q1 Mathematics Pub Date : 2023-11-04 DOI: 10.1016/j.csfx.2023.100101
G. Omel'yanov

We analyze a peakon - antipeakon collision for essentially non-integrable versions of the Camassa-Holm equation. Using the matching and weak asymptotics methods, we construct an asymptotic solution that satisfies both a one-parameter family of equations (with a parameter r), and two energy laws. It is shown that the original waves with amplitudes A1>0 and A2<0 are reflected upon collision and form new waves with amplitudes B1<0 and B2>0 such that, depending on the parameter r, either B1=A2 and B2=A1, or Bi are arbitrary numbers provided B1+B2=A1+A2.

我们分析了本质上不可积的Camassa-Holm方程的一个峰-反峰碰撞。使用匹配和弱渐近方法,我们构造了一个满足单参数方程组(参数为r)和两个能量定律的渐近解。结果表明,振幅为A1>;0和A2<;0在碰撞时被反射并且形成具有振幅B1<;0和B2>;0,使得根据参数r,B1=A2和B2=A1,或者Bi是任意数字,前提是B1+B2=A1+A2。
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引用次数: 0
Analysis of perturbation factors and fractional order derivatives for the novel singular model using the fractional Meyer wavelet neural networks 用分数阶Meyer小波神经网络分析奇异模型的扰动因子和分数阶导数
Q1 Mathematics Pub Date : 2023-08-21 DOI: 10.1016/j.csfx.2023.100100
Zulqurnain Sabir , Mohamed R. Ali

In this study, an analysis of the perturbation factors and fractional order derivatives is performed for the novel singular model. The design of the perturbed fractional order singular model is presented by using the traditional form of the Lane-Emden along with the detail of singular points, fractional order, shape, and perturbed factors. The analysis of the perturbation factors and fractional order terms for the singular model is provided in two steps by taking three different values of the perturbed term as well as fractional order derivatives. The numerical analysis of the perturbation and fractional order terms for the novel fractional Meyer wavelet neural network (FMWNN) along with the global and local search effectiveness of the genetic algorithm (GA) and active-set algorithm (ASA) called as FMWNN-GAASA. The modeling of the FMWNN is presented in terms of mean square error, while the optimization is performed through the GAASA. The authentication, validation, excellence, and correctness of the singular model are observed by using the comparative performances of the obtained and the reference solutions. The stability of the proposed stochastic scheme is observed through the statistical performances for taking large datasets to present the analysis of the perturbation and fractional order terms.

在这项研究中,对新的奇异模型的扰动因子和分数阶导数进行了分析。利用Lane-Emden的传统形式,结合奇异点、分数阶、形状和扰动因子的细节,给出了扰动分数阶奇异模型的设计。通过取扰动项的三个不同值以及分数阶导数,分两步对奇异模型的扰动因子和分数阶项进行分析。对新型分数阶Meyer小波神经网络(FMWNN)的扰动项和分数阶项的数值分析,以及遗传算法(GA)和称为FMWNN-GAASA的主动集算法(ASA)的全局和局部搜索有效性。FMWNN的建模是根据均方误差进行的,而优化是通过GAASA进行的。通过使用所获得的解和参考解的比较性能,观察了奇异模型的认证、验证、卓越性和正确性。通过采用大数据集来分析扰动项和分数阶项的统计性能,观察了所提出的随机方案的稳定性。
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引用次数: 0
Public goods games played on hypergraphs, by agents with bounded learning and planning 具有有限学习和规划的代理人在超图上玩的公共产品游戏
Q1 Mathematics Pub Date : 2023-08-08 DOI: 10.1016/j.csfx.2023.100099
Prakhar Godara, Stephan Herminghaus

Public goods games between model agents with bounded rationality and a simple learning rule, which have been previously shown to represent experimentally observed human playing behavior, are studied by direct simulation on various lattices with different network topology. Despite strong coupling between playing groups, we find that average investments do not significantly depend upon network topology, but are determined solely by immediate local network environment. Furthermore, the dependence of investments on characteristic agent parameters factorizes into a function of individual cognitive budget, K, and a simple function 1/(1+c(0)/β), where c(0) is the group centrality and β=12.5 for all networks investigated. Given the good agreement of agent behavior with available experiments, this seems to indicate that even complex societal networks of investment in public goods may be accessible to predictive simulation with limited effort.

通过在不同网络拓扑的各种网格上的直接模拟,研究了具有有限理性和简单学习规则的模型代理之间的公共产品博弈,这些模型代理先前已被证明代表了实验观察到的人类游戏行为。尽管游戏组之间有很强的耦合性,但我们发现平均投资并不显著依赖于网络拓扑,而是完全由直接的本地网络环境决定。此外,投资对特征代理参数的依赖性被分解为个体认知预算的函数K和简单函数1/(1+c(0)/β),其中c(O)是群体中心性,对于所研究的所有网络,β=12.5。鉴于代理人行为与现有实验的良好一致性,这似乎表明,即使是公共产品投资的复杂社会网络,也可以通过有限的努力进行预测模拟。
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引用次数: 0
期刊
Chaos, Solitons and Fractals: X
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