Triptycenes have been established as unique scaffolds because of their backbone ?-structure with a propeller-like shape and saddle-like cavities. They are some the key organic molecules that extensively studied in polymer chemistry, supramolecular chemistry material science. become chiral when substituents unsymmetrically attached at least two different aromatic rings. This Minireview highlight...

Many chaotic oscillators have coherent phase dynamics but strong fluctuations in the amplitudes. At variance with such a behavior, homoclinic chaos is characterized by quite regular spikes but strong fluctuation in their time intervals due to the chaotic recurrence to a saddle point. We study influences of noise on homoclinic chaos. We demonstrate both numerically and experimentally on a CO2 la...

In this work we characterize in detail the bifurcation leading to an excitable regime mediated by localized structures in a dissipative nonlinear Kerr cavity with a homogeneous pump. Here we show how the route can be understood through a planar dynamical system in which a limit cycle becomes the homoclinic orbit of a saddle point (saddle-loop bifurcation). The whole picture is unveiled, and the...

Abstract: Infinite-horizon problems of kinds that arise in macroeconomic applications present a challenge in optimal control which has only partially been met. Results from the theory of convex problems of Lagrange can be utilized, to some extent, the most interesting feature being that in these problems the analysis revolves about a rest point of the Hamiltonian, which is at the same time a sa...

We investigate the influence of intrinsic noise on stable states of a one-dimensional dynamical system that shows in its deterministic version a saddle-node bifurcation between monostable and bistable behaviour. The system is a modified version of the Schlögl model, which is a chemical reaction system with only one type of molecule. The strength of the intrinsic noise is varied without changing...

We propose a class of regularized Hermitian and skew-Hermitian splitting methods for the solution of large, sparse linear systems in saddle-point form. These methods can be used as stationary iterative solvers or as preconditioners for Krylov subspace methods. We establish unconditional convergence of the stationary iterations and we examine the spectral properties of the corresponding precondi...

Traveling fronts are shown to occur in an array of nearest-neighbor coupled symmetric bistable units. When the local dynamics is given by the Lorenz equations we observe the route: standing-->oscillating-->traveling front, as the coupling is increased. A key step in this route is a gluing bifurcation of two cycles in cylindrical coordinates. When this is mediated by a saddle with real leading e...

Marvelous bending/straightening effects of two-way shape memory alloy (TWSMA) help their employment in design and manufacturing of new medical appliances. Constrained ageing with bending load scheme can induce two-way shape memory effect (TWSME). Scanning electron microscope (SEM) analysis, electrical resistivity measurement (ERM) and differential scanning calorimetry (DSC) are employed to dete...

The authors discuss cloud droplet activation and deactivation in terms of saddle-node bifurcation. By doing so they can employ a nonlinear dynamic approach to study the properties of such processes. Specifically, they approximate the drop growth by diffusion equation to a normal form of a saddle-node bifurcation (df/dt = a + fËĘ2) and therefore they could use the properties of such form to stud...