Quadratization refers to a transformation of an arbitrary system of polynomial ordinary differential equations to a system with at most quadratic right-hand side. Such a transformation unveils new variables and model structures that facilitate model analysis, simulation, and control and offers a convenient parameterization for data-driven approaches. Quadratization techniques have found applications in diverse fields, including systems theory, fluid mechanics, chemical reaction modeling, and mathematical analysis. In this study, we focus on quadratizations that preserve the stability properties of the original model, specifically dissipativity at given equilibria. This preservation is desirable in many applications of quadratization including reachability analysis and synthetic biology. We establish the existence of dissipativity-preserving quadratizations, develop an algorithm for their computation, and demonstrate it in several case studies.

翻译：二次化是指将任意多项式常微分方程组转化为右端项至多为二次的系统的一种变换。这种变换揭示了新的变量和模型结构，有助于模型分析、仿真和控制，并为数据驱动方法提供了便捷的参数化形式。二次化技术已在系统理论、流体力学、化学反应建模和数学分析等多个领域得到应用。本研究聚焦于能够保持原模型稳定性特性（特别是给定平衡点处的耗散性）的二次化方法。这种保持特性在二次化的许多应用中（包括可达性分析和合成生物学）具有重要意义。我们证明了耗散保持型二次化的存在性，开发了相应的计算算法，并通过多个案例研究进行了验证。