Preventive and Reactive Cyber Defense Dynamics with Ergodic Time-dependent Parameters Is Globally Attractive

2020/01/22 by Han, Yujuan, Lu, Wenlian, Xu, Shouhuai · 2 citations
#Cryptography and Security (cs.CR) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Social and Information Networks (cs.SI)

paper · doi:10.48550/arxiv.2001.07958

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.

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