Complex dynamics and synchronization of delayed-feedback nonlinear oscillators

We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos. The oscillator uses electro-optic modulation and fibre-optic transmission, with feedback and filtering implemented through real-time digital signal processing. We consider two such oscillators that are coupled to one another, and we identify the conditions under which they will synchronize. By examining the rates of divergence or convergence between two coupled oscillators, we quantify the maximum Lyapunov exponents or transverse Lyapunov exponents of the system, and we present an experimental method to determine these rates that does not require a mathematical model of the system. Finally, we demonstrate a new adaptive control method that keeps two oscillators synchronized, even when the coupling between them is changing unpredictably.

• Publication year

  2009

• Venue

  Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

• Publication date

  2009-08-06

• Fields of study

  Mathematics, Physics, Medicine, Engineering

• Identifiers
  DOI 10.1098/rsta.2009.0225arXiv 0908.0936PMID 20008405
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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