Scalar observations from a class of high-dimensional chaotic systems: Limitations of the time delay embedding

The time delay embedding for the reconstruction of a state space from scalar data introduces strong folding of the smooth manifold in which a chaotic attractor is embedded, which is absent in some more natural state space. In order to observe the deterministic nature of data, the typical length scale related to this folding has to be resolved. Above this length scale the data appear to be random. For a particular model class we prove these statements and we derive analytically the dependence of this length scale on the complexity of the system. We show that the number of scalar observations required to observe determinism increases exponentially in the product of the system's entropy and dimension. (c) 1997 American Institute of Physics.     

Photochemische Synthesen potentiell hypoglykämisch wirkender 3-Oxazoline

Photochemical Syntheses of 3-Oxazolines which Possibly Exhibit Hypoglycemic Activity Reactions of photochemically generated benzonitrile methylides 2 with carbonyl compounds 3 yielded 3-oxazolines of the types 5 and 6 (Scheme 1). Photooxidation of 5-[p-(dimethylamino)phenyl]-2,2-dimethyl-4-phenyl-3-oxazoline ( 5a ) gave 4′-(2,2-dimethyl-4-phenyl-3-oxazolin-5-yl)-N-methylformanilide ( 6r ) which could be transformed to 2,2-dimethyl-5-[p-(methylamino)phenyl]-4-phenyl-3-oxazoline ( 6s ) by photodecarbonylation. Thirty 3-oxazolines of types 5 and 6 have been synthesized and tested by oral and/or intraperitoneal administration to starved rats and obese-hyperglycemic mice.     

Chimeras in leaky integrate-and-fire neural networks: effects of reflecting connectivities

The effects of attracting-nonlocal and reflecting connectivity are investigated in coupled Leaky Integrate-and-Fire (LIF) elements, which model the exchange of electrical signals between neurons. Earlier investigations have demonstrated that repulsive-nonlocal and hierarchical network connectivity can induce complex synchronization patterns and chimera states in systems of coupled oscillators. In the LIF system we show that if the elements are nonlocally linked with positive diffusive coupling on a ring network, the system splits into a number of alternating domains. Half of these domains contain elements whose potential stays near the threshold and they are interrupted by active domains where the elements perform regular LIF oscillations. The active domains travel along the ring with constant velocity, depending on the system parameters. When we introduce reflecting coupling in LIF networks unexpected complex spatio-temporal structures arise. For relatively extensive ranges of parameter values, the system splits into two coexisting domains: one where all elements stay near the threshold and one where incoherent states develop, characterized by multi-leveled mean phase velocity profiles.     

Failure of feedback as a putative common mechanism of spreading depolarizations in migraine and stroke

The stability of cortical function depends critically on proper regulation. Under conditions of migraine and stroke a breakdown of transmembrane chemical gradients can spread through cortical tissue. A concomitant component of this emergent spatio-temporal pattern is a depolarization of cells detected as slow voltage variations. The propagation velocity of approximately 3 mm/min indicates a contribution of diffusion. We propose a mechanism for spreading depolarizations (SD) that rests upon a nonlocal or noninstantaneous feedback in a reaction-diffusion system. Depending upon the characteristic space and time scales of the feedback, the propagation of cortical SD can be suppressed by shifting the bifurcation line, which separates the parameter regime of pulse propagation from the regime where a local disturbance dies out. The optimization of this feedback is elaborated for different control schemes and ranges of control parameters.     

Einsteinian gravity from a topological action

The curvature-squared model of gravity, in the affine form proposed by Weyl and Yang, is deduced from a topological action in 4D. More specifically, we start from the Pontrjagin (or Euler) invariant. Using the BRST antifield formalism with a double duality gauge fixing, we obtain a consistent quantization in spaces of double dual curvature as classical instanton type background. However, exact vacuum solutions with double duality properties exhibit a ‘vacuum degeneracy’. By modifying the duality via a scale breaking term, we demonstrate that only Einstein’s equations with an induced cosmological constant emerge for the topology of the macroscopic background. This may have repercussions on the problem of ‘dark energy’ as well as ‘dark matter’ modeled by a torsion induced quintaxion.     

Chimera states in networks of logistic maps with hierarchical connectivities

Chimera states are complex spatiotemporal patterns consisting of coexisting domains of coherence and incoherence. We study networks of nonlocally coupled logistic maps and analyze systematically how the dilution of the network links influences the appearance of chimera patterns. The network connectivities are constructed using an iterative Cantor algorithm to generate fractal (hierarchical) connectivities. Increasing the hierarchical level of iteration, we compare the resulting spatiotemporal patterns. We demonstrate that a high clustering coefficient and symmetry of the base pattern promotes chimera states, and asymmetric connectivities result in complex nested chimera patterns.     

Strong and weak chaos in nonlinear networks with time-delayed couplings

We study chaotic synchronization in networks with time-delayed coupling. We introduce the notion of strong and weak chaos, distinguished by the scaling properties of the maximum Lyapunov exponent within the synchronization manifold for large delay times, and relate this to the condition for stable or unstable chaotic synchronization, respectively. In simulations of laser models and experiments with electronic circuits, we identify transitions from weak to strong and back to weak chaos upon monotonically increasing the coupling strength.     

Synchronization scenarios of chimeras in multiplex networks

Complex networks consisting of several interacting layers allow for remote synchronization of distant layers via an intermediate relay layer. We extend the notion of relay synchronization to chimera states, and study the scenarios of relay synchronization in a three-layer network of FitzHugh–Nagumo (FHN) oscillators, where each layer has a nonlocal coupling topology. Varying the coupling strength and time delay in the inter-layer connections, we observe relay synchronization between chimera states, i.e., complex spatio-temporal patterns of coexisting coherent and incoherent domains, in the outer network layers. Special regimes where only the coherent domains of chimeras are synchronized, and the incoherent domains remain desynchronized, as well as transitions between different synchronization regimes are analyzed.