Basically, LIAPOUNOV's stability implies that variations in the initial conditions do not change the qualitative behavior of the system, i.e. allowing for definite phase transitions between a limited number of qualified possible states.
J.L. CHABERT and A.D. DALMEDICO write: "POINCARÉ considered also another concept of stability, which was make clearer somewhat later on by the Russian mathematician LYAPUNOV, and which concerns the difference between a periodic trajectory and the neighbouring ones: if the difference diminishes the trajectory is stable. The solutions are stable or unstable in relation to certain coefficients which typify them, the "characteristic exponents" (1991, p.570).
These are known as "LYAPUNOV exponents" and defines trajectories which maybe asymptotic, periodic or chaotic.
- 1) General information
- 2) Methodology or model
- 3) Epistemology, ontology and semantics
- 4) Human sciences
- 5) Discipline oriented
To cite this page, please use the following information:
Bertalanffy Center for the Study of Systems Science (2020). Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]
We thank the following partners for making the open access of this volume possible: