Reviews of resilience theories and mathematical generalization

This chapter presents a comprehensive review of the resilience theories developed in three key fields of study or systems, namely, socioecological systems, sociotechnical systems and computer systems. Having thus clarified the nature of the resilience approach and its target function, a mathematical generalization of the resilience theories is established. A theoretical work on solving nonlinear dynamic problems using a two-step approach is also reviewed in order to expand the solution tools for studying system behaviors of complex dynamical systems, which are the targets of resilience studies. In order to reflect the latest research, several recent technical books and monographs on the subject are used as the basis of discussion. These are: Biggs et al., Principles for Building Resilience: Sustaining Ecosystem Services in Social–Ecological Systems, edited by Biggs et al. (2015), Resilience Engineering in Practice: A Guidebook, edited by Hollnagel, Paries, Woods and Wreathall (2011); and Resilient Computer System Design by Castano and Schagaev (2015). The following reviews are basically summaries and digests of the resilience theories and practices introduced in these books, with some comments by Z. Shi.