Information transfer as a new indicator of approaching local bifurcations: saddle-node, pitchfork and Hopf bifurcations

Abstract

Early warning signals are key tools for anticipating qualitative changes in the dynamics of complex systems. In this work, we investigate whether an information-theoretic measure designed to characterize directional causal dependencies between observables can provide early warning of the approach to bifurcations. The measure considered is the rate of information transfer, which has been successfully applied to characterize directional dependencies in a broad range of fields, from economics to climate science. Three fundamental local bifurcations are considered: saddle-node, pitchfork, and Hopf bifurcations. We first investigate idealized (quasi-)potential stochastic systems for which analytical expressions for the rate of information transfer can be derived. Distinct signatures are found for the three bifurcation types. In particular, the rate of information transfer displays a strong increase and divergence when approaching the saddle-node bifurcation, whereas smoother but systematic changes are found near the pitchfork and Hopf bifurcations. The approach is then tested using low-order climate models exhibiting the same types of bifurcations. The results confirm that changes in the rate of information transfer can precede the corresponding dynamical transitions, suggesting that directional information transfer provides a useful complementary early-warning indicator for detecting the approach to critical transitions in nonlinear stochastic systems.