Self-generation of microwave nonlinear waveforms in the magnonic-optoelectronic oscillator (MOEO) was investigated. Nonlinear dynamics of the MOEO was due to both optical and magnonic paths of the oscillator circuit. Four-magnon parametric interactions in the magnonic path and cosine transfer function of the electro-optical modulator caused double nonlinearity of the MOEO. Gain coefficient was used as a control parameter. We found that during a route from regular to chaotic dynamics, the oscillator generates two unusual waveforms: symmetry-breaking soliton-like modes of Möbius type and periodic pulses with chaotic amplitude modulation. Nonlinear waveforms were characterized using a time series analysis. Peculiarities of the signals and their spectra in regular and chaotic regimes of self-generation are discussed. We expect that the multiple nonlinearity of the MOEO may be useful for investigation of various fundamental effects in complex time-delayed systems and for development of novel circuits for neuromorphic computing.
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