Modern society depends on stability and high performance of multiple complex infrastructures. Examples of these critical infrastructures include power grids, communication or transportation networks. As the loss of their functionality can lead to serious economic and social consequences, understanding vulnerabilities of these complex systems is of the utmost importance for decision makers of our society. Many real world complex systems can be modeled as complex networks, thus providing convenient modeling framework for vulnerabilities of these systems. Most of the existing studies measure vulnerabilities of complex network to different attacks by assuming underlying network with static nodes and links, where node (or link) failure results in a permanent loss of its functionalities. Furthermore, current studies analyse only the effects of different attack types on targeted networks, but fail to study the effects on the external attacking network itself. Extending theory and concepts in the field of complex networks, this thesis models and evaluates vulnerabilities of dynamic complex networks with local-dependencies and active recovery process to cascade failures caused by continuous ongoing time-dependent attacks and by consequences of initiating an attack on a competing network. The proposed vulnerability models of complex networks form a core basis for the design methodology and stability analysis of future emerging socio-technical systems - the systems in which various technologies are intertwined with people, social and organization structures so that all of them mutually interact and influence each other.