Chaotic attractor  simulation :

• Equations used in paper for simulation of chaotic attractor :  DDE simulation equations.  

• 3D  projection of attractor in reconstructed embedding phase space  [St(n),St(n-1),St(n-2)] :

Attractor of transmitted '0' - red.
Attractor of transmitted '1' - blue .

• Zooming  into  attractor  :

Attractor of transmitted '0' - red.
Attractor of transmitted '1' - blue .

• Each trajectory starts at a random initial state  :

In order to confuse unauthorized receiver, each trajectory starts at a random initial state. Shown below is the superposition of many trajectories that start at a random initial state and converge to the same attractor .

• Dynamics is chaotic  :

The dynamics is chaotic. Shown are two diverging trajectories that are initially separated with a distance 0.0001 .

• A more complicated  attractor  :

At the moment we examine various types of attractors to enhance security and efficiency of DDE.
Attractor of transmitted '0' - red.
Attractor of transmitted '1' - blue .

• Zooming  into  attractor  :

Attractor of transmitted '0' - red.
Attractor of transmitted '1' - blue .


Clearly , reconstruction of the attractor position is a  (very ) hard task , not knowing the dynamics of the receiver and simulating the system in order to find the attractor position.