Toward Analytical Chaos in Nonlinear Systems

Proof

The proof of this theorem is similar to the proof of Theorem 3.10.

Consider quasi-periodic flows in periodically forced, time-delayed nonlinear systems, and the analytical solution of quasi-periodic motion relative to period-m flow is stated from the following theorem.

Theorem 4.6

Consider a periodically forced, time-delayed, nonlinear system as

4.142

where is a -continuous nonlinear function vector with forcing period .

1. If such a time-delayed dynamical system has a period-m flow with finite norm and period , there is a generalized coordinate transformation with for the period- ...