Phase effects on synchronization by dynamical relaying in delay-coupled systems

Synchronization in an array of mutually coupled systems with a finite time delay in coupling is studied using the Josephson junction as a model system. The sum of the transverse Lyapunov exponents is evaluated as a function of the parameters by linearizing the equation about the synchronization manifold. The dependence of synchronization on damping parameter, coupling constant, and time delay is studied numerically. The change in the dynamics of the system due to time delay and phase difference between the applied fields is studied. The case where a small frequency detuning between the applied fields is also discussed.

Some Results on Reciprocal Subtangent in the Context of Weighted Models

Recently, reciprocal subtangent has been used as a useful tool to describe the behaviour of a density curve. Motivated by this, in the present article we extend the concept to the weighted models. Characterization results are proved for models viz. gamma, Rayleigh, equilibrium, residual lifetime, and proportional hazards. An identity under weighted distribution is also obtained when the reciprocal subtangent takes the form of a general class of distributions. Finally, an extension of reciprocal subtangent for the weighted models in the bivariate and multivariate cases are introduced and proved some useful results