Stability domains for time-delay feedback control with latency

We generalize a known analytical method for determining the stability of periodic orbits controlled by time-delay feedback methods when latencies associated with the generation and injection of the feedback signal cannot be ignored. We discuss the case of extended time-delay autosynchronization (ETDAS) and show that nontrivial qualitative features of the domain of control observed in experiments can be explained by taking into account the effects of both the unstable eigenmode and a single stable eigenmode in the Floquet theory.Comment: 9 pages, 6 figures; Submitted to Physical Review

The combinatorics of open covers (II)

We continue to investigate various diagonalization properties for sequences of open covers of separable metrizable spaces introduced in Part I. These properties generalize classical ones of Rothberger, Menger, Hurewicz, and Gerlits-Nagy. In particular, we show that most of the properties introduced in Part I are indeed distinct. We characterize two of the new properties by showing that they are equivalent to saying all finite powers have one of the classical properties above (Hurewicz property in one case and in the Menger property in other). We consider for each property the smallest cardinality of metric space which fails to have that property. In each case this cardinal turns out to equal another well-known cardinal less than the continuum. We also disprove (in ZFC) a conjecture of Hurewicz which is analogous to the Borel conjecture. Finally, we answer several questions from Part I concerning partition properties of covers

Increased tolerance of Litopenaeus vannamei to white spot syndrome virus (WSSV) infection after oral application of the viral envelope protein VP28

It has been generally accepted that invertebrates such as shrimp do not have an adaptive immune response system comparable to that of vertebrates. However, in the last few years, several studies have suggested the existence of such a response in invertebrates. In one of these studies, the shrimp Penaeus monodon showed increased protection against white spot syndrome virus (WSSV) using a recombinant VP28 envelope protein of WSSV. In an effort to further investigate whether this increased protection is limited to P. monodon or can be extended to other penaeid shrimp, experiments were performed using the Pacific white shrimp Litopenaeus vannamei. As found with P. monodon, a significantly lower cumulative mortality for VP28-fed shrimp was found compared to the controls. These experiments demonstrate that there is potential to use oral application of specific proteins to protect the 2 most important cultured shrimp species, P. monodon and L. vannamei, against WSSV. Most likely, this increased protection is based on a shared and, therefore, general defence mechanism present in all shrimp species. This makes the design of intervention strategies against pathogens based on defined proteins a viable option for shrimp cultur

Dynamic Response Analysis of an Icosahedron Shaped Lighter Than Air Vehicle

The creation of a lighter than air vehicle using an inner vacuum instead of a lifting gas is considered. Specifically, the icosahedron shape is investigated as a design that will enable the structure to achieve positive buoyancy while resisting collapse from the atmospheric pressure applied. This research analyzes the dynamic response characteristics of the design, and examines the accuracy of the finite element model used in previous research by conducting experimental testing. The techniques incorporated in the finite element model are confirmed based on the experimental results using a modal analysis. The experimental setup designed will allow future research on the interaction between the frame and skin of icosahedron like structures using various combinations of materials and construction methods. Additionally, a snapback behavior observed in previous static response analysis is further investigated to determine nonlinear instability issues with the design. Dynamic analysis of the structure reveals chaotic motion is present in the frame of the icosahedron under certain loads and boundary conditions. These findings provide information critical to the design of an icosahedron shaped lighter than air vehicle using an inner vacuum

Coexisting patterns of population oscillations: the degenerate Neimark Sacker bifurcation as a generic mechanism

We investigate a population dynamics model that exhibits a Neimark Sacker bifurcation with a period that is naturally close to 4. Beyond the bifurcation, the period becomes soon locked at 4 due to a strong resonance, and a second attractor of period 2 emerges, which coexists with the first attractor over a considerable parameter range. A linear stability analysis and a numerical investigation of the second attractor reveal that the bifurcations producing the second attractor occur naturally in this type of system.Comment: 8 pages, 3 figure

Dense, sequentially continuous maps on dyadic compacta

AbstractWe prove in ZFC that for every sequentially continuous ω-dense function f which maps a dyadic compactum onto a Tychonoff space Y, there exists a closed subspace Z ⊆ Dτ such that f[Z] = f[Dτ] and the restriction of f to Z is continuous. Moreover, the range of every such mapping f is a dyadic compactum

Visibility graphs and symbolic dynamics

Visibility algorithms are a family of geometric and ordering criteria by which a real-valued time series of N data is mapped into a graph of N nodes. This graph has been shown to often inherit in its topology non-trivial properties of the series structure, and can thus be seen as a combinatorial representation of a dynamical system. Here we explore in some detail the relation between visibility graphs and symbolic dynamics. To do that, we consider the degree sequence of horizontal visibility graphs generated by the one-parameter logistic map, for a range of values of the parameter for which the map shows chaotic behaviour. Numerically, we observe that in the chaotic region the block entropies of these sequences systematically converge to the Lyapunov exponent of the system. Via Pesin identity, this in turn suggests that these block entropies are converging to the Kolmogorov- Sinai entropy of the map, which ultimately suggests that the algorithm is implicitly and adaptively constructing phase space partitions which might have the generating property. To give analytical insight, we explore the relation k(x), x \in[0,1] that, for a given datum with value x, assigns in graph space a node with degree k. In the case of the out-degree sequence, such relation is indeed a piece-wise constant function. By making use of explicit methods and tools from symbolic dynamics we are able to analytically show that the algorithm indeed performs an effective partition of the phase space and that such partition is naturally expressed as a countable union of subintervals, where the endpoints of each subinterval are related to the fixed point structure of the iterates of the map and the subinterval enumeration is associated with particular ordering structures that we called motifs