Answer :
An equilibrium point in state space is one where the rates of change for all state variables are zero (the state-space is the space for which each state variable is an axis).
The equilibrium index of an array is an index such that the sum of items at lower indices equals the total of elements at higher indexes.The signs of the eigenvalues of the linearization of the equations concerning the equilibria can be used to classify equilibria. That is, the equilibria may be classified by evaluating the Jacobian matrix at each of the system's equilibrium points and then calculating the resultant eigenvalues. The behavior of the system in the vicinity of each equilibrium point may then be qualitatively (or even statistically, in certain cases) identified by locating the eigenvector(s) associated with each eigenvalue. If none of the eigenvalues have a zero real component, the equilibrium point is hyperbolic. The point is stable if all eigenvalues have negative real portions. The point is unstable if at least one has a positive real component.
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