WOLFRAM|DEMONSTRATIONS PROJECT

Recurrence Network Measures for the Logistic Map

​
network measure
degree
clustering
control parameter a
3.75
recurrence threshold ϵ
0.05
The degree centrality and clustering coefficient of nodes in the recurrence network of a time series reveal complementary geometrical properties of the dynamics in phase space. This helps to distinguish between the various dynamical regimes of a complex nonlinear system.
The logistic map provides a good model for dynamical transitions among regular, laminar, and chaotic behavior of a dynamical system. The evolution and properties of the time series depend on the control parameter
a
.
Observe how the degree and clustering series and frequency distribution evolve as you change the control parameter
a
. Can you identify periodic windows in a sea of chaos? As you increase the recurrence threshold
ϵ
, the recurrence network measures slowly approach those expected for a fully connected network.