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Canard-Tipping Cascades in adaptive dynamical networks
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Date
2026-06-30
Authors
Luddy, Adam
Journal Title
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Publisher
University College Cork
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Abstract
A tipping point is a strong instability that involves a large, sudden, and often unexpected change in the state of a complex system. A tipping-point cascade is a series of tipping points in a network of coupled systems. Despite their prominence in coupled climate and ecological systems, tipping-point cascades remain largely unexplored. One might naively assume that these cascades always occur between distinct stable states, but this is not necessarily the case. In fact, somewhat counter-intuitively, a network can robustly tip between unstable states during a tipping-point cascade. This type of tipping-point cascade was first seen in the phenomenon of Canard Cascading.
In this thesis, we examine non-standard tipping-point cascades in a class of slow-fast adaptive dynamical networks, where robust heteroclinic connections enable a series of fast transitions between coexisting saddle states with slow dynamics. We refer to this novel phenomenon as a Canard-Tipping Cascade (CTC) and demonstrate that it occurs robustly in different networks and for a large set of parameter values. We also relate CTCs to the recently reported phenomenon of Canard Cascading.
In particular, we present an ecological example of a CTC: a slow-fast adaptive dynamical network of competitive Lotka--Volterra systems. Furthermore, we discuss candidate equations for the minimal or canonical model exhibiting CTCs in order to gain a better understanding of its fundamental properties. We demonstrate that this canonical model can exhibit both (i) the standard bifurcation-induced tipping (B-tipping) cascade between coexisting alternative stable states and (ii) the non-standard CTC between coexisting saddle states.
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Keywords
Dynamical systems , Adaptive networks , Slow-fast systems , Canards
Citation
Luddy, A. 2026. Canard-Tipping Cascades in adaptive dynamical networks. MRes Thesis, University College Cork.