Preventive and Reactive Cyber Defense Dynamics with Ergodic Time-dependent Parameters Is Globally Attractive
Abstract
Cybersecurity dynamics is a mathematical approach to modeling and analyzing cyber attack-defense interactions in networks. In this paper, we advance the state-of-the-art in characterizing one kind of cybersecurity dynamics, known as preventive and reactive cyber defense dynamics, which is a family of highly nonlinear system models. We prove that this dynamics in its general form with time-dependent parameters is globally attractive when the time-dependent parameters are ergodic, and is (almost) periodic when the time-dependent parameters have the stronger properties of being (almost) periodic. Our results supersede the state-of-the-art ones, including that the same type of dynamics but with time-independent parameters is globally convergent.
Keywords
Cite
@article{arxiv.2001.07958,
title = {Preventive and Reactive Cyber Defense Dynamics with Ergodic Time-dependent Parameters Is Globally Attractive},
author = {Yujuan Han and Wenlian Lu and Shouhuai Xu},
journal= {arXiv preprint arXiv:2001.07958},
year = {2020}
}