Preventive and Reactive Cyber Defense Dynamics With Ergodic Time-Dependent Parameters is Globally Attractive
Yujuan Han, Wenlian Lu, Shouhuai Xu · IEEE Transactions on Network Science and Engineering · 2021
Cybersecurity dynamics is a mathematical approach to modeling and analyzing cyber attacker-defender interactions in networks. In this paper, we advance the state-of-the-art in characterizing one kind of cybersecurity dynamics, known aspreventive and reactive cyber defense dynamics, which is a family of highly nonlinear dynamical system models. We prove that this family of dynamics in its general form withtime-dependentparameters isglobally attractivewhen the time-dependent parameters areergodic, and is(almost) periodicwhen the time-dependent parameters have the stronger properties of being(almost) periodic. Our results supersede the state-of-the-art ones, including the recent result that the same family of dynamics in the special case oftime-independentparameters isglobally convergent. This paper represents a significant advance in the network science approach to theoretical cybersecurity modeling because it makes the so-far weakest assumptions when compared with the literature results.