IDC402 Non Linear Dynamics

Wednesday, February 2, 2022

Mechanisms to get an odd period

Third kind of [2022-01-18#Bifurcations|bifurcation] - Tangent Bifurcation, Saddle node bifurcation

No solutions $\to$ 2 solutions, of which 1 is stable and 1 is unstable.

Intermittency

[2022-02-02#Intermittency|Intermittency last class]

Structure within this region

• [2022-01-27#Figenbaum scaling] is still retained.
• Period doubling also occurs

Organisation and Appearance of Periodic Orbits

$3, 5, 7, …$ $2*3, 2*5, 2*7, …$ $2^2*3, 2^2*5, …$ $…$ $…2^3, 2^2, 2^1, 1$

Orbits of a map $F$ will come in the reverse order. Hence, Period 3 implies chaos.