Saturation and Survival: Why Some Organizations Persist and Others Collapse

This paper applies Stuart-Landau dynamics to organizational survival, demonstrating that thesaturation parameter β determines long-term viability. Organizations with β > 0 possessinternal growth limits and can reach stable equilibria; organizations with β → 0 requireunbounded growth and inevitably collapse when external constraints intervene. We analyzetwo contrasting cases: a technology company whose business model assumes unlimitedscaling (β → 0), and an entertainment company whose model incorporates natural saturation(β > 0). The analysis predicts that the former will experience catastrophic failure while thelatter will persist through market fluctuations. This is not a contingent prediction but astructural consequence: systems without saturation mechanisms cannot achieve stableequilibria and must either grow indefinitely or collapse. Since indefinite growth is physicallyimpossible, collapse is certain.