If an equilibrium point belongs to the Pareto boundary, the equilibrium is said to be efficient.
First, a third-order linear system is designed to ensure that its unique equilibrium point belongs to a saddle-focus type with index 2 and the corresponding eigenvalues satisfy Shilnikov conditions.
Proposition 3. If one of the two sets of conditions (15) holds, equilibrium A3 belongs to Ω.
The Jacobian around A2 is hence the analysis of the corresponding linear system leads to proposition 2. Proposition 2. 1) If γ > δ, equilibrium A2 belongs to Ω.
From this viewpoint, the pseudo-equilibrium models belong to the most advanced tools of SBSP.
Moreover, there is a transition among the equilibrium state, quasi-equilibrium state, and non-equilibrium state, e.g., Figure 〈11〉 in Figure 4b belongs to quasi-equilibrium state of non-equilibrium state.
Equilibrium A2 exists and belongs to Ω if γ > δ.
Note that, setting S ~ i 0 as the initial search space for the bioSDP algorithm we are focusing the analysis on those equilibrium points that belong to a neighborhood of x e i, instead of searching for all the equilibrium points.
However, in general, some equilibrium problems always belong to different subsets of spaces, so the SEP is important and quite general.
If a target equilibrium point of a domain Dij belongs to Dij, it corresponds to a stable equilibrium point of the system.
