Dynamics of Some Perturbed Morse-Type Oscillators: Simulations and Applications

Abstract

The purpose of this paper is to investigate some Morse-type oscillators. In its original form, it is a model for describing the vibrations of a diatomic molecule. The Morse potential generalizes the harmonic oscillator by introducing deviations from the classical theoretical model. In the present study, we perturbed the Morse differential equation by several periodic terms based on the cosine function and by a damping term. The frequency is driven by different coefficients. The size of the deviations is controlled by another constant. We provide two modifications w.r.t. the damping term. The Melnikov approach is applied as an indicator of the possible chaotic opportunities. We also propose a novel approach for stochastic control of the perturbations. It is based on the assumption that the coefficients of the periodic terms are the probabilities of underlying distribution. As a result, the dynamics are driven by its characteristic function. Several applications are considered. We demonstrate some specialized modules for investigating the dynamics of the proposed models, along with the synthesis of radiating antenna patterns.

Keywords

• Morse-type oscillator
• Melnikov’s approach
• Melnikov function
• Melnikov antenna array