Table 3.

Detailed characteristics of the non-chaotic, quasi-periodic signals.

Symbol	Properties				Sample signal	Sample phase portrait
QPS_145	Name	Quasi-periodic 1			Fig. 21	Fig. 22
	Class	quasi-periodic	Dim	1
	Params	ω1 = π
	Init. cond.	x0 = 2π, Tmax = 1000
	State eqn.	$x=cos\left({\omega }_{1}t/50+x_0\right)+cos\left(t/50+x_0\right)$
	Descr.	Irrational ω ratio: ω1/ω2 = π
QPS_246	Name	Quasi-periodic 2			Fig. 23	Fig. 24
	Class	quasi-periodic	Dim	1
	Params	${\omega }_1=\left(1+\sqrt{5}\right)/2$
	Init. cond.	x0 = 2π, Tmax = 1000
	State eqn.	$x=sin\left({\omega }_{1}t/15+x_0\right)+sin\left(t/15+x_0\right)$
	Descr.	Irrational ω golden ratio: ${\omega }_1/{\omega }_2=\phi =\left(1+\sqrt{5}\right)/2$
QPS_347	Name	Quasi-periodic 3			Fig. 25	Fig. 26
	Class	quasi-periodic	Dim	1
	Params	ω1 = e = 2.71828…
	Init. cond.	x0 = 2π, Tmax = 1000
	State eqn.	$x=sin\left({\omega }_{1}t/15+x_0\right)+cos\left(t/15+x_0\right)$
	Descr.	Irrational ω ratio: ω1/ω2 = e = 2.71828…