A bivariate catastrophe model for non-orthogonal decentralized digital currencies

The increasing integration of cryptocurrencies into global financial markets has created new channels of systemic fragility, driven not only by extreme volatility but also by increasingly strong cross-asset interdependencies. This paper develops a bivariate extension of the cusp catastrophe model to analyze the nonlinear joint dynamics of two major cryptocurrencies — Bitcoin and Ethereum — during the March 2020 crash. By introducing a contagion term into the coupled potential function, the model captures how inter-asset feedback loops deform the joint stability landscape, generating coordinated bifurcations, co-jumps, and abrupt transitions across equilibrium states. Empirical estimation using log-returns from January to June 2020 shows that both assets operated near the fold manifold of the bivariate catastrophe surface, with the interaction parameter λ remaining statistically significant and temporally stable across subsamples. Bootstrap inference and Monte Carlo simulations confirm the robustness of the coupling structure and indicate that extreme movements in one cryptocurrency propagate nonlinearly to the other. Sensitivity analysis reveals that large values of λ steepen the joint potential surface and enlarge the region of negative Hessian determinant, thereby amplifying systemic instability. These findings suggest that the March 2020 collapse corresponds to a joint loss of stability rather than independent crashes in separate markets. Policy implications follow directly from the geometry of the model: coordinated circuit breakers, liquidity buffers, and real-time monitoring of the Hessian structure can help shift the system away from bifurcation boundaries. Overall, the study underscores that catastrophe theory provides a mathematically grounded and empirically valid framework for analyzing instability and contagion in decentralized digital-asset ecosystems.