Two-dimensional phase-space picture of the photonic crystal Fano laser

The recently realized photonic crystal Fano laser constitutes the first demonstration of passive pulse generation in nanolasers [Nat. Photonics $\boldsymbol{11}$, 81-84 (2017)]. We show that the laser operation is confined to only two degrees-of-freedom after the initial transition stage. We show that the original 5D dynamic model can be reduced to a 1D model in a narrow region of the parameter space and it evolves into a 2D model after the exceptional point, where the eigenvalues transition from being purely to a complex conjugate pair. The 2D reduced model allows us to establish an effective band structure for the eigenvalue problem of the stability matrix to explain the laser dynamics. The reduced model is used to associate a previously unknown origin of instability with a new unstable periodic orbit separating the stable steady-state from the stable periodic orbit.Comment: 12 pages, 7 figures, journal, Phys. Rev. A, before editorial correctio

Dynamics of Mutualism in a Two Prey, One Predator System with Variable Carrying Capacity

We considered the livelihood of two prey species in the presence of a predator species. To understand this phenomenon, we developed and analyzed two mathematical models considering indirect and direct mutualism of two prey species and the influence of one predator species. Both types of mutualism are represented by an increase in the preys\u27 carrying capacities based on direct and indirect interactions between the prey. Because of mutualism, as the death rate parameter of the predator species goes through some critical value, the model shows transcritical bifurcation. Additionally, in the direct mutualism model, as the death rate parameter decreases to some critical value, the model shows limit cycle phenomena

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal