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Background: Defining the optimal conduction of percutaneous-coronary-intervention (PCI) to treat bifurcation lesions has been the subject of many clinical studies showing that the applied stenting technique may influence clinical outcome. Accordingly, bifurcation stenting classifications and technical sequences should be standardized to allow proper reporting and comparison. Methods: The European Bifurcation Club (EBC) is a multidisciplinary group dedicated to optimize the treatment of bifurcations and previously created a classification of bifurcation stenting techniques that is based on the first stent implantation site. Since some techniques have been abandoned, others have been refined and dedicated devices became available, EBC promoted an international task force aimed at updating the classification of bifurcation stenting techniques as well as at highlighting the best practices for most popular techniques. Original descriptive images obtained by drawings, bench tests and micro-computed-tomographic reconstructions have been created in order to serve as tutorials in both procedure reporting and clinical practice. Results: An updated Main-Across-Distal-Side (MADS)-2, classification of bifurcation stenting techniques has been realized and is reported in the present article allowing standardized procedure reporting in both clinical practice and scientific studies. The EBC-promoted task force deeply discussed, agreed on and described (using original drawings and bench tests) the optimal steps for the following major bifurcation stenting techniques: (a) 1-stent techniques (“provisional” and “inverted provisional”) and (b) 2-stent techniques (“T/TAP,” “culotte,” and “DK-crush”). Conclusions: The present EBC-promoted paper is intended to facilitate technique selection, reporting and performance for PCI on bifurcated lesions during daily clinical practice.

We consider discrete dynamical systems coming from the models of evolution of populations playing rock - paper - scissors game . Asymptotic behaviour of trajectories of these systems is described, occurrence of the Neimark-Sacker bifurcation and nonexistence of time averages are proved.

In this study, we investigate a discrete-time version of logit dynamics, as applied to the rock–paper–scissors (RPS) game. First, we show that around the Nash equilibrium point, an attracting closed invariant curve appears due to the Neimark–Sacker bifurcation. Next, near the resonance point, we find a period-three attracting cycle, which can be thought of as a counterpart to the cyclically stable set in the RPS game with best response dynamics. Moreover, we show that the cycle can coexist with an attracting closed invariant curve, a period-three saddle cycle, and the attracting or repelling Nash equilibrium point. Finally, we use the codimension-two bifurcation theory to specify the set of heteroclinic bifurcations that destroy the coexistence of the attractors.

In this paper we propose a statistical approach for the optimization of the phased codes used in radar. By considering each code as a realization of a random variable we show that we can build good codes if the distribution of the random variable is suitably chosen. We then consider sequences generated by the skew tent map and we show that for some values of the bifurcation parameter the invariant probability density coincides with the desired one. To confirm this idea we compute the maximal peak of the ambiguity function outside zero relative to the bifurcation parameter of the skew tent map.

In the commented paper, the authors considered a two-dimensional airfoil with nonlinear stiffness and damping, and derived the amplitude modulation equation (AME) of the system limit cycle oscillation around its bifurcation. Based on the variation equation of the AME, they conducted the stability analysis. Unfortunately, the obtained variation equation associated with the AME is incorrect.

We investigate the dynamics of three-strategy (rock–paper–scissors) replicator equations in which the fitness of each strategy is a function of the population frequencies delayed by a time interval $$T$$ . Taking $$T$$ as a bifurcation parameter, we demonstrate the existence of (non-degenerate) Hopf bifurcations in these systems and present an analysis of the resulting limit cycles using Lindstedt’s method.

We present a novel paper-based flow fractionation system for preconcentration and field-flow separation. In this passive fluidic device, a straight channel is divided into multiple daughter channels, each of which is connected with an expanded region. The hydrodynamic resistance of the straight channel is predominant compared with those of expanded regions, so we can create steady flows through the straight and daughter channels. While the expanded regions absorb a great amount of water via capillarity, the steady flow continues for 10 min without external pumping devices. By controlling the relative hydrodynamic resistances of the daughter channels, we successfully divide the flow with flow rate ratios of up to 30. Combining this bifurcation system with ion concentration polarization (ICP), we develop a continuous-flow preconcentrator on a paper platform, which can preconcentrate a fluorescent dye up to 33-fold. In addition, we construct a field-flow separation system to divide two different dyes depending on their electric polarities. Our flow fractionation systems on a paper-based platform would make a breakthrough for point-of-care diagnostics with specific functions including preconcentration and separation.

We investigate a population of individuals who play the Rock–Paper–Scissors (RPS) game. The players choose strategies not only by optimizing their payoffs, but also taking into account the popularity of the strategies. For the standard RPS game, we find an asymptotically stable polymorphism with coexistence of all strategies. For the general RPS game we find the limit cycles. Their stability depends exclusively on two model parameters: the sum of the entries of the RPS payoff matrix, and a sensitivity parameter which characterizes the personality of the players. Apart from the supercritical Hopf bifurcation, we found the subcritical bifurcation numerically for some intervals of the parameters of the model.

In this work, important aspects of bacteriocin producing bacteria and their interplay are elucidated. Various attempts to model the resistant, producer and sensitive Escherichia coli strains in the so-called rock-scissors-paper (RSP) game had been made in the literature. The question arose whether there is a continuous model with a cyclic structure and admitting an oscillatory dynamics as observed in various experiments. The May-Leonard system admits a Hopf bifurcation, which is, however, degenerate and hence inadequate. The traditional differential equation model of the RSP-game cannot be applied either to the bacteriocin system because it involves positive interaction terms. In this paper, a plausible competitive Lotka-Volterra system model of the RSP game is presented and the dynamics generated by that model is analyzed. For the first time, a continuous, spatially homogeneous model that describes the competitive interaction between bacteriocin-producing, resistant and sensitive bacteria is established. The interaction terms have negative coefficients. In some experiments, for example, in mice cultures, migration seemed to be essential for the reinfection in the RSP cycle. Often statistical and spatial effects such as migration and mutation are regarded to be essential for periodicity. Our model gives rise to oscillatory dynamics in the RSP game without such effects. Here, a normal form description of the limit cycle and conditions for its stability are derived. The toxicity of the bacteriocin is used as a bifurcation parameter. Exact parameter ranges are obtained for which a stable (robust) limit cycle and a stable heteroclinic cycle exist in the three-species game. These parameters are in good accordance with the observed relations for the E. coli strains. The roles of growth rate and growth yield of the three strains are discussed. Numerical calculations show that the sensitive, which might be regarded as the weakest, can have the longest sojourn times.

In a preceding paper of Jin and Wang the authors describe computations concerning differential systems of the form x=y, y=-x+a 1 x 2 +a 2 xy+a 3 y 2 +a 4 x x3 +a 5 x 2 y+a 6 xy 2 +a 7 y 3 . We give proofs of the results suggested by these computations and provide a full description of the bifurcation of small-amplitude limit cycles in a subclass of these systemes

We study the Turing instability to stationary spatial patterns in reaction-transport systems with inertia. After a brief discussion of hyperbolic reaction-diffusion equations and reaction-Cattaneo equations we focus on reaction random walks, which are the most natural generalization of reaction-diffusion equations. We analyze the effect of inertia in the transport on spatial instabilities of the homogeneous steady state. Direction-dependent reaction walks, where the interaction between particles depends on the direction in which the particles are moving, allow us to take account of an energy requirement for reactive interactions, i.e., an activation energy, in the reaction-transport equation. We compare bifurcation conditions for direction-independent reaction walks and for direction-dependent reaction walks to assess the effect of inertia in the transport and the effect of activation energies in the kinetics on the Turing instability.© (2005) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Using the conservation of complex power technique (CCPT), this paper presents a solution to the problem of EM scattering at the junction of a parallel-plate waveguide and an N-furcated parallel-plate waveguide with arbitrarily spaced thick septa. Although this junction can be regarded as an (N + 1)-port configuration, the problem is formulated so that it is viewed mathematically as a generalized 2-port. This leads to very simple expressions for the scattering parameters of the junction. Convergent numerical results are presented for bifurcated, trifurcated, and 4-furcated structures, and the effects of varying the thickness of the septa are investigated. The formulation is directly applicable to N-furcated rectangular waveguide junctions having TE/sub n0/ excitation, with application in the design of E-plane filters.

Coronavirus disease 2019 is a recent strong challenge for the world. In this paper, an epidemiology model is investigated as a model for the development of COVID-19. The propagation of COVID-19 through various sub-groups of society is studied. Some critical parameters, such as the background of mortality without considering the disease state and the speed of moving people from infected to resistance, affect the conditions of society. In this paper, early warning indicators are used to predict the bifurcation points in the system. In the interaction of various sub-groups of society, each sub-group can have various parameters. Six cases of the sub-groups interactions are studied. By coupling these sub-groups, various dynamics of the whole society are investigated.

The ecological theory of species interactions rests largely on the competition, interference, and predator–prey models. In this paper, we propose and investigate a three-species predator–prey model to inspect the mutual interference between predators. We analyze boundedness and Kolmogorov conditions for the non-spatial model. The dynamical behavior of the system is analyzed by stability and Hopf bifurcation analysis. The Turing instability criteria for the Spatio-temporal system is estimated. In the numerical simulation, phase portrait with time evolution diagrams shows periodic and chaotic oscillations. Bifurcation diagrams show the very rich and complex dynamical behavior of the non-spatial model. We calculate the Lyapunov exponent to justify the dynamics of the non-spatial model. A variety of patterns like interference, spot, and stripe are observed with special emphasis on Beddington–DeAngelis function response. These complex patterns explore the beauty of the spatio-temporal model and it can be easily related to real-world biological systems.

Dengue is a mosquito-borne disease which has continued to be a public health issue in Malaysia. This paper investigates the impact of singular use of vaccination and its combined effort with treatment and adulticide controls on the population dynamics of dengue in Johor, Malaysia. In a first step, a compartmental model capturing vaccination compartment with mass random vaccination distribution process is appropriately formulated. The model with or without imperfect vaccination exhibits backward bifurcation phenomenon. Using the available data and facts from the 2012 dengue outbreak in Johor, basic reproduction number for the outbreak is estimated. Sensitivity analysis is performed to investigate how the model parameters influence dengue disease transmission and spread in a population. In a second step, a new deterministic model incorporating vaccination as a control parameter of distinct constant rates with the efforts of treatment and adulticide controls is developed. Numerical simulations are carried out to evaluate the impact of the three control measures by implementing several control strategies. It is observed that the transmission of dengue can be curtailed using any of the control strategies analysed in this work. Efficiency analysis further reveals that a strategy that combines vaccination, treatment and adulticide controls is most efficient for dengue prevention and control in Johor, Malaysia.