According to Lyapunov stability theory, several sufficient conditions for the network to achieve cluster mixed synchronization are derived.
In order to obtain sufficient data for the network training, numerical simulation was used to simulate different ranges of misfires in the engine.
One significant feature of the two-stage filtering schemes discussed above is that the consensus communication occurs at a much shorter time scale than the operation of local filters, i.e., it is assumed that there is sufficient time for the network to achieve consensus through intensive inter-node communications before the arrival of the next observation.
Furthermore, we develop a phase space representation, focusing on the inputs to and the intrinsic slow variable of the knee extensor motoneuron, which we use to derive sufficient conditions for the network to realize each rhythm and which illustrates the role of a saddle-node bifurcation in achieving the knee extensor delay.
This heuristic is imperfect, but is sufficient for all the networks in Figure 3, which are also all homomorphisms (the simplest kind of morphisms).
By employing Halanay-type inequalities, some sufficient conditions for the networks to be globally exponentially stable are also derived.
By constructing suitable Lyapunov functionals, the delay-independent sufficient conditions for the networks converge exponentially towards the equilibrium associated with the constant input are obtained.
Studies by Draznin et al. [ 38] and Bergouignan et al. [ 39] suggest that CHO restriction alone, and even in the presence of caloric overconsumption, is sufficient for the activation of this network in human muscle cells, in line with the finding that AMPK is sensitive not only to the intracellular ATP/AMP ratio, but also to glycogen stores [ 40].
The question will be how many intensely loyal users can Paper find, and will the small but active fraction of Facebook's total 1.28 billion users be enough to produce sufficient engagement for the social network to keep supporting its reader app.
On Sure Start, he said the budget was "going up" from £2,212m to £2,297m and said the chief executive of the Daycare Trust, Anand Shukla, had said the government had "allocated sufficient funding for the existing network of Sure Start children's centres to be maintained".
