Fluctuational escape from a quasi-hyperbolic attractor in the Lorenz system

Noise-induced escape from the basin of attraction of a quasi-hyperbolic chaotic attractor in the Lorenz system is considered. The investigation is carried out in terms of the theory of large fluctuations by experimentally analyzing the escape prehistory. The optimal escape trajectory is shown to be unique and determined by the saddle-point manifolds of the Lorenz system. We established that the escape process consists of three stages and that noise plays a fundamentally different role at each of these stages. The dynamics of fluctuational escape from a quasi-hyperbolic attractor is shown to differ fundamentally from the dynamics of escape from a nonhyperbolic attractor considered previously [1]. We discuss the possibility of analytically describing large noise-induced deviations from a quasi-hyperbolic chaotic attractor and outline the range of outstanding problems in this field.     

Evaluation of high-performance liquid chromatography with a dual working-electrode electrochemical detector for the determination of catecholamines in human cerebrospinal fluid

A procedure is described for quantifying norepinephrine [1(3,4-dihydroxyphenyl)-2-aminoethanol] and dopamine (4-(2-aminoethyl)-1,2-benzenediol] in cerebrospinal fluid by high-performance liquid chromatography (h.p.l.c.) with dual working-electrode electrochemical detection. An ion-pairing reversed-phase h.p.l.c. technique is used after clean-up and preconcentration of the fluid on alumina. The dual working-electrode electrochemical detector used provides amplification in the electrochemical response per unit concentration of material passing through the detector. This is achieved by locating two working electrodes on the opposite walls of a thin-layer cell, holding them close together and at potentials that will induce a sequence of oxidation/reductions. The greater the number of oxidation/reduction cycles, the greater the amplification of the electrochemical response. Peak height ratios are linear over the range expected and detection limits are 3 pg for norepinephrine and 5 pg for dopamine. The concentrations of norepinephrine and dopamine in human cerebrospinal fluid were found to be 141 pg ml^?1 and 262 pg ml^?1 with relative standard deviations of 6.8 and 5.8%, respectively.     

Synthesis of 1-substituted benzo[c]isoxazol-3(1H)-imines via tandem nitroso-ene/intramolecular cyclizations of 2-nitrosobenzonitrile

Instead of reacting via the expected coarctate cyclization pathway, 2-nitrosobenzonitrile undergoes a tandem nitroso-ene/intramolecular cyclization to form benzo[c]isoxazol-3(1H)-imines in very good yields under neutral conditions and at moderate temperatures. Treatment of three of the imines with HBF4 results in dimerization/condensation to furnish unusual, delocalized cationic systems.     

Inference of a nonlinear stochastic model of the cardiorespiratory interaction

We reconstruct a nonlinear stochastic model of the cardiorespiratory interaction in terms of a set of polynomial basis functions representing the nonlinear force governing system oscillations. The strength and direction of coupling and noise intensity are simultaneously inferred from a univariate blood pressure signal. Our new inference technique does not require extensive global optimization, and it is applicable to a wide range of complex dynamical systems subject to noise.