Mixed-mode oscillations in slow-fast delayed optoelectronic systems

Area of Science:

• Nonlinear Dynamics
• Optoelectronics
• Complex Systems

Background:

• Breathers are complex oscillatory phenomena observed in various physical systems.
• Optoelectronic oscillators exhibit rich dynamical behaviors, including oscillations.
• Mixed-mode oscillations (MMOs) represent a class of complex dynamics characterized by the coexistence of different types of oscillations.

Purpose of the Study:

• To investigate the dynamical behavior of breathers in optoelectronic oscillators.
• To understand the emergence of breather dynamics through the lens of mixed-mode oscillations.
• To develop an analytical framework for characterizing breather phenomenology.

Main Methods:

• Analysis of breather dynamics from the perspective of mixed-mode oscillations.
• Phase space analysis to identify key features of breather behavior.
• Development of an analytical framework using the Liénard reduction form.

Main Results:

• Breathers in optoelectronic oscillators are identified as composite oscillations damped to attractive branches of an invariant manifold.
• The emergence of breather dynamics is directly linked to the appearance of inflection points in the phase space.
• The developed analytical framework provides significant insight into the underlying phenomenology.

Conclusions:

• The study establishes a clear connection between breather dynamics, mixed-mode oscillations, and phase space inflection points in optoelectronic oscillators.
• Theoretical predictions derived from the Liénard reduction form show excellent agreement with experimental measurements.
• This work offers a robust analytical approach to understanding complex oscillatory phenomena in optoelectronic systems.