计算机病毒的计算分析的随机分数顺序模型
Armughan Ayaz1, Muhammad Aziz Ur Rehamn1, Muhammad Rafiq2
1Department of Mathematics, University of Management and Technology, Lahore, 54782, Pakistan.
Scientific reports
|October 1, 2025
概括
这项研究引入了一种新的分数顺序模型来分析计算机病毒的传播,将内存效应和随机影响纳入更现实的数字感染动态.
科学领域:
- 数学建模的数学建模
- 计算机病毒学 计算机病毒学
- 网络安全 网络安全
背景情况:
- 传统的整数顺序模型无法捕捉数字感染固有的记忆和持久性.
- 现有的研究往往忽视了病毒传播中随机性和分数动态的综合效应.
研究的目的:
- 为分析计算机病毒传播动态开发一种新的分数顺序数学框架.
- 扩展模型以纳入随机影响,反映现实世界的网络复杂性.
- 严格分析模型的属性,包括解决方案的存在,独特性和稳定性.
主要方法:
- 使用卡普托的分数导数重新构建经典的整数顺序模型.
- 应用巴纳赫定点定理来确定解决方案的存在和独特性.
- 通过引入白噪声术语来扩展随机分数模型.
- 基于格伦瓦尔德-莱特尼科夫的非标准有限差异方案的开发,用于数值近似.
主要成果:
- 分数计算机病毒模型成功地捕获了内存和持久性特征.
- 对模型的两个平衡状态进行了全球稳定性分析.
- 随机分数模型确保了独特的可解决性,解决了组合的记忆和随机性.
- 数字模拟验证了理论发现,证明了复杂的动态.
结论:
- 拟议的分数顺序和随机模型为了解计算机病毒传播提供了一个强大而现实的框架.
- 这种方法提高了在复杂的网络环境中数字感染动态的预测.
- 该研究强调了考虑记忆效应和随机性对于准确的病毒传播分析的重要性.
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