ABSTRACT
We investigate synchronization in complex networks of noisy phase oscillators. We find that, while too weak a coupling is not sufficient for the whole system to synchronize, too strong a coupling induces a nontrivial type of phase slip among oscillators, resulting in synchronization failure. Thus, an intermediate coupling range for synchronization exists, which becomes narrower when the network is more heterogeneous. Analyses of two noisy oscillators reveal that nontrivial phase slip is a generic phenomenon when noise is present and coupling is strong. Therefore, the low synchronizability of heterogeneous networks can be understood as a result of the difference in effective coupling strength among oscillators with different degrees; oscillators with high degrees tend to undergo phase slip while those with low degrees have weak coupling strengths that are insufficient for synchronization.
ABSTRACT
The phenomenon of slow switching in populations of globally coupled oscillators is discussed. This characteristic collective dynamics, which was first discovered in a particular class of the phase oscillator model, is a result of the formation of a heteroclinic loop connecting a pair of clustered states of the population. We argue that the same behavior can arise in a wider class of oscillator models with the amplitude degree of freedom. We also argue how such heteroclinic loops arise inevitably and persist robustly in a homogeneous population of globally coupled oscillators. Although a heteroclinic loop might seem to arise only exceptionally, we find that it appears rather easily by introducing time delay into a population which would otherwise exhibit perfect phase synchrony. We argue that the appearance of the heteroclinic loop induced by the delayed coupling is then characterized by transcritical and saddle-node bifurcations. Slow switching arises when a system with a heteroclinic loop is weakly perturbed. This will be demonstrated with a vector model by applying weak noises. Other types of weak symmetry-breaking perturbations can also cause slow switching.
ABSTRACT
The kinetics (absorption, distribution and excretion) of carteolol were investigated after oral and intravenous administration to man, rats, Beagle dogs and rabbits. The half-life of carteolol in plasma was 1.22 approximately 1.45 hr in rats, 1.73 approximately 2.08 hr in dogs and 1.42 approximately 1.43 hr in rabbits, and was independent of the route of administration. The absorption rate constants, obtained from log(C1-C) approximately time plot, after oral administration were 1.89 hr-1 in rats, 1.04 hr-1 in dogs and 1.54 hr-1 in rabbits. There were no differences between tablet and film coated tablet in the pharmacokinetic parameters of carteolol in man after oral 30 mg (tablet or film coated tablet) administration [half life (t1/2)=4.50 hr (tablet), 4.30 hr (film coated tablet), elimination rate constant (k2) equals 0.154 hr-1 (tablet), 0.161 hr-1 (film coated tablet)]. The elimination rate constant, obtained from Sigma-minus plot after 2, 5 and 10 mg oral administration, was 0.137 approximately 0.160 hr-1.
