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Preventive and Reactive Cyber Defense Dynamics With Ergodic Time-Dependent Parameters is Globally Attractive
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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… Click to show full abstract
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 as preventive 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 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 the recent result that the same family of dynamics in the special case of time-independent parameters is globally 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.
