AI Insight
This paper introduces "viability space decomposition" (VSD), a new mathematical framework for analyzing ordinary differential equation models of biological agents subject to survival constraints. By identifying novel classes of manifolds (mortality, ordering, and collapse), VSD partitions the entire state space into regions with qualitatively distinct survival outcomes, producing what the authors call a "viability portrait." The framework is demonstrated on three progressively complex models: a subcellular biochemical network, a single behaving cell, and a two-coupled-cell network, showing how transient dynamics leading to death can be systematically characterized beyond classical attractors and separatrices.
Why it matters
This framework could improve the analysis of survival-critical biological systems across multiple fields, including disease treatment optimization, ecological risk assessment, and the study of adaptive fitness, by providing rigorous tools to map the conditions under which organisms or collectives live or die.
arXiv:2605.16753v1 Announce Type: new
Abstract: What determines whether an organism or collective will survive under particular conditions? This question is asked across the life sciences when determining adaptive fit, developing efficacious treatments for diseases, and assessing the risks posed by ecological shifts. To aid their investigations, researchers employ models of agents which must respect particular constraints to remain alive. By constraining the dynamics of these agents to bounded viability regions, these models form a class of extended dynamical systems where transient dynamics can lead to death, making traditional attractors and separatrices insufficient for characterizing the global space of possible behaviors. To remedy this, we develop viability space decomposition, an analysis framework for ordinary differential equation models of agents with viability constraints. We first introduce the general theory, revealing how several new classes of manifolds (mortality, ordering, and collapse) permit a complete decomposition of state space into regions of qualitatively similar survival outcomes: a viability portrait. We then demonstrate the method by completely analyzing the global behavior of three models: a subcellular network, a behaving cell with the same physiology, and two coupled cell networks. Finally, we finish by discussing how the framework scales and future directions for its development and application.