 The study investigates the dynamics in biological networks, specifically gene regulatory networks, using a coupled map network model. The research aims to design systems that are robust against both phenotypic perturbations, dynamics, and mutation, structure, perturbations. A multi-canonical Monte Carlo method is applied to achieve this goal. The analysis reveals that systems with marginal stability, or those at the edge of chaos, emerge when robustness against network perturbations is necessary. This phenomenon is a self-organization result and does not require fine-tuning of parameters. This article was authored by Nen Saito and Makoto Kikuchi.