From LaSalle invariance principle
, we deduce that [Q.sub.0] is globally asymptotically stable.
By LaSalle's invariance principle
, we get that [E.sub.f] is globally asymptotically stable when [R.sub.0] [less than or equal to] 1.
According to LaSalle's invariance principle
, with arbitrary initial values of the output error dynamical system (5), the trajectories converge asymptotically to the set M, which ensures us the detection quality of the complex network's topology.
Ma designed the study, developed the methodology of invariance principle
, and wrote the manuscript.
Prove Here we use the Lyapunov-LaSalle invariance principle
to prove that [E.sub.0] is overall attracted concerned with [[OMEGA].sub.W [less than or equal to] 1+[epsilon]].
S253), however, "an essential condition for a theory of choice that claims normative status is the principle of invariance: different representations of the same choice problem should yield the same preference." (1,2) In this article, we provide evidence that consumers violate the invariance principle
when making an extremely important financial decision near retirement: when to claim Social Security benefits.
One tool to be used here LaSalle's invariance principle
. If we consider the delay differential system
Equally important in special relativity is the invariance principle
: those different sets of perceptions are the consequence of a common set of physical laws, applicable to all.
It follows from LaSalle invariance principle
 that the infection-free equilibrium [E.sup.*.sub.0] is globally asymptotically stable.
In Section 3, by structuring suitable Lyapunov functionals and using LaSalle's invariance principle
we attain the global stability of the uninfected equilibrium if [R.sub.0] [less than or equal to] 1.
Further, by using the well-known Lyapunov-Lasalle invariance principle
, we prove the global asymptotic stability of the infection-free equilibrium, CTL-absent infection equilibrium, and a special case of CTL-present equilibrium.
The convergence analysis is then obtained via an extending LaSalle invariance principle
for impulsive systems in .