IDC402 Non Linear Dynamics

Wednesday, February 2, 2022

Mechanisms to get an odd period

Third kind of [bifurcation] - Tangent Bifurcation, Saddle node bifurcation

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

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

$3,5,7,\dots$ $2\ast 3,2\ast 5,2\ast 7,\dots$ $2^2\ast 3,2^2\ast 5,\dots$ $\dots$ $\dots 2^3,2^2,2^1,1$

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