PERIODIC SOLUTION OF THE BLACK BODY OSCILLATOR EQUATION

Abstract

The main purpose of the present paper is to obtain an existence-uniqueness of periodic solution of the black body oscillator equation. Here we replace the classical radiation term by the relativistic form of the Dirac’s radiation term proposed in a previous our paper. We use an operator presentation of the periodic problem and by means of a fixed point method we prove an existence-uniqueness of periodic solution. As a consequence, we show that Ehrenfest paradox does exist within classical physics but not in relativistic physics.

Periodic oscillation for a coupled ring Stuart-Landau oscillators

Abstract

In this paper, the existence of periodic oscillation of the solutions for a coupled ring Stuart-Landau oscillators model with delays is investigated. Double Hopf bifurcation of coupled dissipative Stuart-Landau oscillators with delay has been investigated in the literature which is very special case because this model considered only one delay. A model includes n different time delays is considered. By the extended Chafee’s criterion, the oscillatory behavior of the Stuart-Landau oscillators model is brought to the instability of the unique equilibrium point and the boundedness of the solutions of the system. Some sufficient conditions to guarantee the oscillation of the solutions which are very easy to check comparing to the bifurcating method are provided. Computer simulations are given to support the present results. Our simulation suggests that synchronization phenomenon occurred, and time delays affect the oscillatory frequency much and amplitude slightly. Keywords: coupled ring Stuart-Landau oscillator, delay, instability, oscillation