Universal scaling properties of type-I intermittent chaos in isolated resistance arteries are unaffected by endogenous nitric oxide synthesis

Formation and destruction of multilayered tori in coupled map systems

The paper first illustrates how multilayered tori can arise through one or more pitchfork bifurcations of the saddle cycle on an ordinary resonance torus. The paper hereafter describes three different scenarios by which a multilayered torus can be destructed. One scenario involves a saddle-node bifurcation in which the middle layer of a three-layered torus disappears in an abrupt transition to chaos while the outer-layer manifolds and their associated saddle and unstable-focus cycles continue to exist and to control the transient dynamics. In a second scenario, the unstable focus cycles of the intermediate layers in a five-layered torus turn into unstable nodes, and closed loop connections are established between the unstable nodes and the points of the stable resonance node on the torus. Finally, a third scenario describes a transition in which homoclinic bifurcations destroy first the outer layers and thereafter also the inner layer. The paper also illustrates how the formation and destruction of multilayered tori can occur in the cluster dynamics of an ensemble of globally coupled maps. This leads to three additional scenarios for the destruction of multilayered tori.

Dynamics of a three-variable nonlinear model of vasomotion: comparison of theory and experiment

The effects of pharmacological interventions that modulate Ca(2+) homeodynamics and membrane potential in rat isolated cerebral vessels during vasomotion (i.e., rhythmic fluctuations in arterial diameter) were simulated by a third-order system of nonlinear differential equations. Independent control variables employed in the model were [Ca(2+)] in the cytosol, [Ca(2+)] in intracellular stores, and smooth muscle membrane potential. Interactions between ryanodine- and inositol 1,4,5-trisphosphate-sensitive intracellular Ca(2+) stores and transmembrane ion fluxes via K(+) channels, Cl(-) channels, and voltage-operated Ca(2+) channels were studied by comparing simulations of oscillatory behavior with experimental measurements of membrane potential, intracellular free [Ca(2+)] and vessel diameter during a range of pharmacological interventions. The main conclusion of the study is that a general model of vasomotion that predicts experimental data can be constructed by a low-order system that incorporates nonlinear interactions between dynamical control variables.

Deterministic nonlinear characteristics ofin vivoblood flow velocity and arteriolar diameter fluctuations

We have performed a nonlinear analysis of fluctuations in red cell velocity and arteriolar calibre in the mesenteric bed of the anaesthetized rat. Measurements were obtained under control conditions and during local superfusion with NG-nitro-L-arginine (L-NNA, 30 microM) and tetrabutylammonium (TBA, 0.1 mM), which suppress NO synthesis and block Ca2+ activated K+ channels (KCa), respectively. Time series were analysed by calculating correlation dimensions and largest Lyapunov exponents. Both statistics were higher for red cell velocity than diameter fluctuations, thereby potentially differentiating between global and local mechanisms that regulate microvascular flow. Evidence for underlying nonlinear structure was provided by analysis of surrogate time series generated from the experimental data following randomization of Fourier phase. Complexity indices characterizing time series under control conditions were in general higher than those derived from data obtained during superfusion with L-NNA and TBA.

Shil'nikov homoclinic chaos is intimately related to type-III intermittency in isolated rabbit arteries: role of nitric oxide

We provide experimental evidence for the existence of Shil'nikov homoclinic chaos in the fluctuations in flow which can be observed in isolated perfused rabbit ear arteries, and establish a close association between homoclinicity and type-III Pomeau-Manneville intermittent behavior. The transition between the homoclinic scenario and type-III intermittency is clarified by a mathematical model of the arterial smooth muscle cell. Simulations of the effects of nitric oxide (NO) by the vascular endothelium on these patterns of behavior closely match experimental observations.