Vulnerability of complex networks due to a parameter drift and strategies to counteract the consequences

• Applicant: Professorin Dr. Ulrike Feudel
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 454054251

The main objective of this proposal is to study the role of a parameter drift on the dynamics of complex networks in the presence of chaotic saddles. Compared to the previous funding period we will now study the vulnerability of networks with respect to two other aspects: While the focus of the previous funding period was on vulnerability of networks with respect to the impact of single perturbations, we will now study the vulnerability of networks with respect to a time-dependent perturbation, i.e., a linear drift of an intrinsic parameter or an external forcing. In addition, we will change the complexity of the internal dynamics of the nodes. Instead of networks, in which each node has only a single attractor, i.e., it is monostable, we now extend our research to multistable systems, where each node can possess a multitude of attractors when uncoupled. In our study we assume that the rate of the parameter drift is of the same order of magnitude as the intrinsic dissipative timescale, i.e. the timescale on which an attractor is approached in the autonomous system. Therefore, this parameter drift has to be taken explicitly into account making the whole system non-autonomous, such that the analysis of its dynamics is far from the classical approach being a simple traversing of a bifurcation diagram. The most important difference compared to autonomous systems is the emergence of a new type of bifurcations, the rate-induced bifurcations in which qualitative changes of the dynamics occur, when the rate of the parameter drift crosses a critical threshold. Specifically, we investigate the modifications to the mechanism of the emergence of chaotic saddles as a result of a basin boundary metamorphosis leading to a shift of the critical parameter value depending on the rate of the parameter drift. Furthermore, we check the hypothesis whether chaotic saddles embedded in the basin boundaries could be ”stabilized” either by a parameter drift or by a non-autonomous control strategy. Applied to large food web models this could establish a novel mechanism of maintaining a high level of biodiversity. In a simpler setup we investigate a complex random network of bistable systems in which rate-induced transitions can lead to tipping cascades, in which - due to uni-directional coupling - one node after another can tip. We study how this process depends on the rate of parameter drift. Furthermore, we develop methods to counteract such tipping cascades to either stop the cascade or even reverse it. Again, the relationship between the different timescales (dissipative timescale, rate of parameter drift and the time horizon of the steering process) will crucially influence the success of controlling the tipping cascade.

• DFG Programme: Research Grants