<p>Chaotic dynamics is of great significance both in addressing the twenty-first century’s fourteenth problem proposed by Smale and in designing complex engineering cybernetic systems. To overcome the limitations of existing chaos criteria that rely on external information, this paper proposes a chaos identification method based exclusively on intrinsic dynamical characteristics. The core idea is inspired by the Cauchy convergence principle, and it demonstrates that chaotic behavior can be identified solely through the dynamical characteristics of the system itself without any external information. By constructing the iterative structure of topological dynamical systems, the localized criteria of multivariate Li–Yorke chaos and multivariate distributional chaos are established, respectively. Specifically, the existence of chaos can be determined by analyzing the local dynamics of the subsystem. It is further proved that these two kinds of chaos can be transformed into each other under appropriate iterative modes, which reveals the intrinsic connections between Li–Yorke chaos and distributional chaos. This research provides a universal theoretical tool for chaotic identification of complex systems.</p>