The phrase "average system is" is correct and usable in written English.
It can be used when discussing the characteristics or performance of a typical system in a specific context.
Example: "In our analysis, we found that the average system is capable of handling multiple tasks simultaneously without significant lag."
Alternatives: "typical system is" or "standard system is".
The fact that our averaged system is derived from a realistic biophysical model has important consequences.
The existence of invariant tori corresponding to periodic orbits in the averaged system is established and their stability is determined.
Then, the dynamical programming equation for the control problems of minimizing the response of the averaged system is formulated based on the dynamical programming principle.
A distributed averaging system is a linear multi-agent system in which agents communicate to reach an agreement (or a consensus) state, defined as the average of the initial states of the agents.
Therefore, the averaged system is defined and bounded on R +.
The averaging system is so complicated that even many insurance agents have difficulty explaining it.
Therefore, if the determinant of the Jacobian is negative (i.e., a fixed point of the averaged system is stable) for functions (f_{a}) and (f_{b}) with constant second derivatives, then when these functions are perturbed in (C^{2}), the Jacobian is negative at the perturbed fixed point (see the previous appendix).
A fixed point ((a^, b^)) of the averaged system is exponentially stable if the Jacobian J = begin{pmatrix} frac{partial F_{a}}{partial a} & frac{partial F_{a}}{partial b} frac{partial F_{b}}{partial a}& frac{partial F_{b}}{partial b} end{pmatrix} evaluated at ((a^, b^)) has two negative eigenvalues.
The fixed point ((a^, b^)) of the averaged system is stable if biggl(frac{partialmu}{partial a}frac{partialnu }{partial b}-frac{partialmu}{partial b}frac{partialnu }{partial a} biggr) biggl(frac{f_{b}"(mu^{f_{b}'(mu^ - frac {f_{a}"(mu^{f_{a}'(mu^ biggr) > varDelta.
The fixed point ((a^, b^)) of the averaged system is stable if biggl(frac{partialmu}{partial a}frac{partialnu }{partial b}-frac{partialmu}{partial b}frac{partialnu }{partial a} biggr) biggl(frac{f_{b}"(mu^{f_{b}'(mu^ - frac {f_{a}"(mu^{f_{a}'(mu^ biggr) > 0. (10).
