Study of the Dynamic Behavior of the Rossler System

a

0.2

b

0.2

c

3.

option

time series

phase space

power spectrum

autocorrelation function

This Demonstration presents the dynamic behavior of the Rossler system, which is governed by

dx

dt

=-y-z

dy

dt

=x+ay

dz

dt

=b+z(x-c).

For a particular selection of the model parameters

a

,

b

, and

c

, you can observe periodic behavior, period doubling, or chaotic behavior. This Demonstration illustrates several important concepts of nonlinear dynamics, such as the time-series plot, phase-space diagram, power spectrum, and autocorrelation function plot.

For

a=b=0.2

and

c=10

, you can observe chaotic behavior, which is confirmed by the power spectrum diagram. The phase space diagram is that of a chaotic attractor.

For

a=b=0.2

and

c=1

, the power spectrum has few discrete bands, which confirms the periodic behavior. Also, a limit cycle is observed in the phase space diagram.