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Network survivability is the ability of a network to stay connected under failures and attacks, which is a fundamental issue to the design and performance evaluation of wireless ad hoc networks. In this paper, we focus on the analysis of network survivability in the presence of node misbehaviors and failures. First, we propose a novel semi-Markov process model to characterize the evolution of node behaviors. As an immediate application of the proposed model, we investigate the problem of node isolation where the effects of denial-of-service (DoS) attacks are considered. Then, we present the derivation of network survivability and obtain the lower and upper bounds on the topological survivability for k-connected networks. We find that the network survivability degrades very quickly with the increasing likelihood of node misbehaviors, depending on the requirements of disjoint outgoing paths or network connectivity. Moreover, DoS attacks have a significant impact on the network survivability, especially in dense networks. Finally, we validate the proposed model and analytical result by simulations and numerical analysis, showing the effects of node misbehaviors on both topological survivability and network performance.