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Robot-assisted laparoscopic pyeloplasty for ureteropelvic junction impediment as a result of aberrant circulatory together with ipsilateral retrocaval ureter.
We study networks of coupled oscillators and analyze the role of coupling delays in determining the emergence of cluster synchronization. Given a network topology and a particular arrangement of the coupling delays over the network connections, different patterns of cluster synchronization may emerge. We focus on a simple ring network of six bidirectionally coupled identical oscillators, for which with two different values of the delays, a total of eight cluster synchronization patterns may emerge, depending on the assignment of the delays to the ring connections. We analyze stability of each of the patterns and find that for large enough coupling strength and specific values of the delays, they can all be stabilized. We construct an experimental ring of six bidirectionally coupled Colpitts oscillators, with delayed connections obtained by coupling the oscillators via RF cables of appropriate length. We find that experimental observations of cluster synchronization are in essential agreement with theoretical predictions. We also verify our theory in a fully connected network of fifty nodes for which connections are randomly assigned to be either undelayed or delayed with a given probability.The aim of this paper is to establish the averaging principle for stochastic differential equations under a general averaging condition, which is weaker than the traditional case. Under this condition, we establish an effective approximation for the solution of stochastic differential equations in mean square.We introduce the Iris billiard that consists of a point particle enclosed by a unit circle around a central scattering ellipse of fixed elongation (defined as the ratio of the semi-major to the semi-minor axes). When the ellipse degenerates to a circle, the system is integrable; otherwise, it displays mixed dynamics. Poincaré sections are presented for different elongations. Recurrence plots are then applied to the long-term chaotic dynamics of trajectories launched from the unstable period-2 orbit along the semi-major axis, i.e., one that initially alternately collides with the ellipse and the circle. We obtain numerical evidence of a set of critical elongations at which the system undergoes a transition to global chaos. The transition is characterized by an endogenous escape event, E, which is the first time a trajectory launched from the unstable period-2 orbit misses the ellipse. The angle of escape, θesc, and the distance of the closest approach, dmin, of the escape event are studied and are shown to be exquisitely sensitive to the elongation. The survival probability that E has not occurred after n collisions is shown to follow an exponential distribution.A system of two identical superconducting quantum interference devices (SQUIDs) symmetrically coupled through their mutual inductance and driven by a sinusoidal field is investigated numerically with respect to dynamical properties such as its multibranched resonance curve, its bifurcation structure and transition to chaos as well as its synchronization behavior. The SQUID dimer is found to exhibit a hysteretic resonance curve with a bubble connected to it through Neimark-Sacker (torus) bifurcations, along with coexisting chaotic branches in their vicinity. Interestingly, the transition of the SQUID dimer to chaos occurs through a torus-doubling cascade of a two-dimensional torus (quasiperiodicity-to-chaos transition). Periodic, quasiperiodic, and chaotic states are identified through the calculated Lyapunov spectrum and illustrated using Lyapunov charts on the parameter plane of the coupling strength and the frequency of the driving field. The basins of attraction for chaotic and non-chaotic states are determined. Bifurcation diagrams are constructed on the parameter plane of the coupling strength and the frequency of the driving field, and they are superposed to maps of the three largest Lyapunov exponents on the same plane. Furthermore, the route of the system to chaos through torus-doubling bifurcations and the emergence of Hénon-like chaotic attractors are demonstrated in stroboscopic diagrams obtained with varying driving frequency. Moreover, asymmetric states that resemble localized synchronization have been detected using the correlation function between the fluxes threading the loop of the SQUIDs.We study the dynamics of a multilayer network of chaotic oscillators subject to amplification. Previous studies have proven that multilayer networks present phenomena such as synchronization, cluster, and chimera states. Here, we consider a network with two layers of Rössler chaotic oscillators as well as applications to multilayer networks of the chaotic jerk and Liénard oscillators. Intra-layer coupling is considered to be all to all in the case of Rössler oscillators, a ring for jerk oscillators and global mean field coupling in the case of Liénard, inter-layer coupling is unidirectional in all these three cases. The second layer has an amplification coefficient. An in-depth study on the case of a network of Rössler oscillators using a master stability function and order parameter leads to several phenomena such as complete synchronization, generalized, cluster, and phase synchronization with amplification. For the case of Rössler oscillators, we note that there are also certain values of coupling parameters and amplification where the synchronization does not exist or the synchronization can exist but without amplification. Using other systems with different topologies, we obtain some interesting results such as chimera state with amplification, cluster state with amplification, and complete synchronization with amplification.Cardiac alternans, a period-2 behavior of excitation and contraction of the heart, is a precursor of ventricular arrhythmias and sudden cardiac death. One form of alternans is repolarization or action potential duration alternans. In cardiac tissue, repolarization alternans can be spatially in-phase, called spatially concordant alternans, or spatially out-of-phase, called spatially discordant alternans (SDA). S(-)-Propranolol molecular weight In SDA, the border between two out-of-phase regions is called a node in a one-dimensional cable or a nodal line in a two-dimensional tissue. In this study, we investigate the stability and dynamics of the nodes and nodal lines of repolarization alternans driven by voltage instabilities. We use amplitude equation and coupled map lattice models to derive theoretical results, which are compared with simulation results from the ionic model. Both conduction velocity restitution induced SDA and non-conduction velocity restitution induced SDA are investigated. We show that the stability and dynamics of the SDA nodes or nodal lines are determined by the balance of the tensions generated by conduction velocity restitution, convection due to action potential propagation, curvature of the nodal lines, and repolarization and coupling heterogeneities.
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