Rate-induced tipping in complex high-dimensional ecological networks

Author:

Panahi Shirin1ORCID,Do Younghae2,Hastings Alan34ORCID,Lai Ying-Cheng15ORCID

Affiliation:

1. School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287

2. Department of Mathematics, Nonlinear Dynamics Mathematical Application Center, Kyungpook National University, Daegu 41566, Republic of Korea

3. Department of Environmental Science and Policy, University of California, Davis, CA 95616

4. Santa Fe Institute, Santa Fe, NM 87501

5. Department of Physics, Arizona State University, Tempe, AZ 85287

Abstract

In an ecosystem, environmental changes as a result of natural and human processes can cause some key parameters of the system to change with time. Depending on how fast such a parameter changes, a tipping point can occur. Existing works on rate-induced tipping, or R-tipping, offered a theoretical way to study this phenomenon but from a local dynamical point of view, revealing, e.g., the existence of a critical rate for some specific initial condition above which a tipping point will occur. As ecosystems are subject to constant disturbances and can drift away from their equilibrium point, it is necessary to study R-tipping from a global perspective in terms of the initial conditions in the entire relevant phase space region. In particular, we introduce the notion of the probability of R-tipping defined for initial conditions taken from the whole relevant phase space. Using a number of real-world, complex mutualistic networks as a paradigm, we find a scaling law between this probability and the rate of parameter change and provide a geometric theory to explain the law. The real-world implication is that even a slow parameter change can lead to a system collapse with catastrophic consequences. In fact, to mitigate the environmental changes by merely slowing down the parameter drift may not always be effective: Only when the rate of parameter change is reduced to practically zero would the tipping be avoided. Our global dynamics approach offers a more complete and physically meaningful way to understand the important phenomenon of R-tipping.

Funder

DOD | USN | ONR | Office of Naval Research Global

National Research Foundation of Korea

Publisher

Proceedings of the National Academy of Sciences

Subject

Multidisciplinary

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