1 / 11

Chaos: Zero lag synchronisation

Chaos: Zero lag synchronisation. Mathijs Vermeulen & Bart van Lith. Contents. Introduction Lang-Kobayashi equations Zero lag synchronization Bernoulli map Perturbed Bernoulli map Conclusions. Introduction.

paxton
Download Presentation

Chaos: Zero lag synchronisation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Chaos: Zero lag synchronisation Mathijs Vermeulen & Bart van Lith

  2. Contents • Introduction • Lang-Kobayashi equations • Zero lag synchronization • Bernoulli map • Perturbed Bernoulli map • Conclusions Don’t panic

  3. Introduction • Paper: Zero Lag Synchronization of Chaotic Systems with Time Delayed Couplings. Englert et al. • Two chaotic semi-conductor lasers are synchronized. • Bernoulli map is investigated analytically. Experimental setup used in the paper. Don’t panic

  4. Lang Kobayashi equations Set of coupled differential equations for that describe the dynamics of a chaotic diode laser. Don’t panic

  5. Experimental data Don’t panic

  6. Bernoulli map • Nonlinear because of the modulo. • Chaotic for α > 1. • Solution • Lyapunov exponent α = 1.5 Don’t panic

  7. Zero lag synchronization • Two signals xt and yt; • Two time delayed couplings with delay time τ1 and τ2; • τ1, τ2 << internal time scales; • Synchronized signals is trivial solution; • Linear stability inspected by adding small perturbation; • Only works if the same mapping is used; • Only works if are prime numbers. Don’t panic

  8. Zero Lag synchronization Don’t panic

  9. Perturbed Bernoulli map • Small non-linear perturbation on Bernoulli map. • ‘Rounds’ the saw-tooth edges. • Works very well for small ε. • Here ε = 0.13, α = 1.5 Don’t panic

  10. Perturbed Bernoulli map α = 1.5, ε = -1.7 Don’t panic

  11. Conclusions • Small perturbations in ZLS are damped if: • Coupling time constants are smaller than internal time scales; • the coupling time constants are prime numbers; • The same mapping is used; • Works for small perturbations in the Bernouilli mapping. Don’t panic

More Related