Piecewise linear feedback rules and weird quasiperiodic dynamics: Some general observations and two economic applications

• We examine piecewise linear feedback in otherwise linear dynamical systems. • Piecewise linear feedback rules can generate weird quasiperiodic attractors. • Weird quasiperiodic attractors help explain fluctuations in economic systems. • Such attractors may be desirable when they replace divergent dynamics. • Such attractors may be undesirable when they suppress fixed-point dynamics. We show that regulators who use piecewise linear feedback rules to stabilize the dynamics of otherwise linear discrete dynamical systems of dimension two or higher may (unintentionally) trigger weird quasiperiodic dynamics. This recently discovered type of behavior, which blends features of both quasiperiodic and chaotic motion, may be desirable when it replaces divergent dynamics or undesirable when it suppresses fixed-point dynamics. After demonstrating that weird quasiperiodic dynamics emerge as a surprisingly natural phenomenon in such systems, an observation relevant to many applied disciplines, we discuss how they may arise in economic contexts, using two economic models as examples. In doing so, we uncover novel sources of endogenous fluctuations in dynamic (economic) systems.