Preventive and Reactive Cyber Defense Dynamics with Ergodic Time-dependent Parameters Is Globally Attractive
This work provides a theoretical foundation for cybersecurity modeling, addressing the need for more realistic time-varying parameters in network defense analysis.
The paper tackled the problem of modeling cyber attack-defense interactions by proving that preventive and reactive cyber defense dynamics with ergodic time-dependent parameters are globally attractive, superseding prior results that only showed convergence for time-independent parameters.
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.