A Minimal Theoretical Model for Morphodynamic Selection in Soft Matter Systems

Abstract

Soft matter systems often display shape transitions, mode competition, and threshold-like dynamical responses driven by the coupling between mechanics, geometry, and biochemical or active fields. Here we present a minimal theoretical framework for describing such morphodynamic selection using a small number of physically interpretable order parameters. The model combines elastic relaxation, active driving, and nonlinear feedback, yielding distinct regimes corresponding to weak deformation, single-mode selection, and coupled shape transformation. We derive the governing equations, identify the relevant dimensionless control parameters, and show how the phase behavior can be organized in terms of threshold competition and effective coupling strengths. The framework provides a compact route for connecting analytical theory, numerical simulations, and experimentally observable shape dynamics in soft and biological matter.