Stability of a state

A general criterion for stability of a state is given by the Lyapunov function. A physical system x may be defined by an m dimensional vector with elements of x, (/ = 1, 2,. .., m) and parameters a, and we have... 

For time-independent boundary conditions, we have the general conditions for the stability of a state... 

The concept of stability of a state of equilibrium is a relative notion. That stability is understood in relation to a specific transformation. For example, if we take oxygenated water at standard temperature and pressure (STP), we know that this substance is unstable in terms of water but is stable in terms of the hydrogen-oxygen mixture. 

The stability of the stationary state can be understood by looking at the behavior of a small perturbation 6Z. To establish the stability of a state, first a positive function L(8X) of 6X, which may be called a distance, is defined in the space spanned by Xu. If this distance between Xgk and the perturbed state (Xfjt + hXk) steadily decreases in time, the stationary state is stable. Thus state Xsk is stable if... 

Note that external self-determination cannot necessarily be seen as being contrary to the predetermined values of peace and stability. Prolonged conflicts about external self-determination could be a bigger threat to peace and stability of a state than an act of secession. 

State Considerations Just like participation strengthens the stability of a state it does not threaten the state. Integration of minorities in majority structures while respecting their identity is one way of strengthening ties between the minority and the majority. Participation aims at common interests and togetherness. There is no external dimension in this on the contrary it strengthens the state intemally as minorities can live acceptably within the existing state. 

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