Resilience and complex dynamics - safeguarding local stability against global instability

We evaluate Brunnermeir’s Theory of Resilience in the context of complex system dynamics where there, however, can be local and global resilience, vulnerability, loss of resilience, cycles, disruptive contractions, and persistent traps. In the paper, we refer to three-time scales. First, for shorter time scales, for the short-run market dynamics, we evaluate resilience in the context of complex market dynamics that have been studied in the history of economic theory for long. Second, with respect to a business cycle medium-term dynamics, we analytically study an endogenous cycle model, built upon Semmler and Sieveking (1993) and Semmler and Kockesen (2017), and discuss the issue of loss of stability, corridor stability, multiple attractors, and trapping dynamics also in the light of complex dynamics. In a financial-real business cycle model, we demonstrate forces that indeed can exhibit multiple dynamic features such as local resilience, known as corridor-stability, but also other dynamic phenomena. Corridor stability pertains to small shocks with no lasting effects, but large enough shocks can lead to persistent cycles and/or contractions. We refer to the Hopf-and-Bautin-Bifurcation theorems, to establish corridor stability, and local resilience, for the interaction of real and financial variables where the trajectories can be stable or unstable in the vicinity of the equilibrium. Thus they can switch dynamic behaviour for small or large shocks. Similar complex dynamic phenomena can be obtained from Kaleckian-Kaldorian nonlinear real business cycle models, in particular when time delays are allowed for. Third, whereas the analytical study of the dynamics is undertaken for the above second-time scale, for the longer time scale we study, in the context of multiple equilibria models, the issue of thresholds, tipping points and disruptive contractions, and persistence of traps.