Coherent Wall Structures: Dynamics and Contribution to Turbulent Activity - Transport and Coherent Structures in Wall Turbulence - page 265

dx

( )

1,2

=− ω y − z + Cxx −

1, 2 1, 2 1, 2 2 ,1 1, 2

dt
dy

1,2

=− ω x y +

1, 2 1, 2 1, 2

dt
dz

( )

1, 2

=+ dz x c −

1, 2 1, 2

dt

ω =±Δ 1

1,2

The dynamic equations governing the first and the second
Rössler oscillator correspond, respectively, to the indices 1
and 2. The coupling between the two systems occurs by way
of the last term in the equation dx 1, 2 dt . The parameters

0.15 , and c 10 are fixed for both oscillators. The

e = =

d = 0.2

coupling C varies and

Δ= 0.015 . The system's phase

()

and

φ t

()

amplitude At are determined using the concept of an

analytical signal [PAP 82].

Figure 4.37. Perfect phase synchronization between two coupled Rössler
oscillators. This figure is adapted from [ROS 96]. See the text of that
publication for details