. 2023 Feb 7;10:79. doi: 10.1038/s41597-023-01978-7

Table 1.

Detailed characteristics of chaotic signals.

Symbol	Properties				Sample signal	Sample phase portrait
CHA_1³⁵ A.4.5	Name	Ueda oscillator			Fig. 1	Fig. 2
	Class	chaotic	Dim	2
	Params	b = 0.05, A = 7.5, Ω = 1
	Init. cond.	x₀ = [2.5, 0], T_max = 100
	State eqn.	${\dot{x}}_{1} = x_{2}$
	State eqn.	${\dot{x}}_{2} = - x_{1}^{3} - b x_{2} + A s i n (Ω t)$
	Descr.	Driven dissipative flow
CHA_2³⁶ A.5.1	Name	Lorenz attractor			Fig. 3	Fig. 4
	Class	chaotic	Dim	3
	Params	$σ = 10, β = 8 / 3, ρ = 28$
	Init. cond.	x₀ = [10, 200, 10], T_max = 100
	State eqn.	${\dot{x}}_{1} = - σ x_{1} + σ x_{2}$
		${\dot{x}}_{2} = ρ x_{1} - x_{2} - x_{1} x_{3}$
		${\dot{x}}_{3} = - β x_{3} + x_{1} x_{2}$
	Descr.	Autonomous dissipative flow
CHA_3³⁷ A.5.2	Name	Rössler attractor			Fig. 5	Fig. 6
	Class	chaotic	Dim	3
	Params	$a = 0.2, b = 0.2, c = 5.7$
	Init. cond.	x₀ = [−9, 0, 0], T_max = 300
	State eqn.	${\dot{x}}_{1} = - x_{2} - x_{3}$
		${\dot{x}}_{2} = x_{1} + a x_{2}$
		${\dot{x}}_{3} = b + x_{3} (x_{1} - c)$
	Descr.	Autonomous dissipative flow
CHA_4³⁸ A.5.13	Name	Halvorsen attractor			Fig. 7	Fig. 8
	Class	chaotic	Dim	3
	Params	$a = 1.27$
	Init. cond.	x₀ = [−5, 0, 0], T_max = 50
	State eqn.	${\dot{x}}_{1} = - a x_{1} - 4 x_{2} - 4 x_{3} - x_{2}^{2}$
		${\dot{x}}_{2} = - 4 x_{1} - a x_{2} - 4 x_{3} - x_{3}^{2}$
		${\dot{x}}_{3} = - 4 x_{1} - 4 x_{2} - a x_{3} - x_{1}^{2}$
	Descr.	Autonomous dissipative flow (cyclically symmetric attractor)
CHA_5³⁹ A.5.15	Name	Rucklidge attractor			Fig. 9	Fig. 10
	Class	chaotic	Dim	3
	Params	k = 2, λ = 6.7
	Init. cond.	x₀ = [1, 0, 4.5], T_max = 150
	State eqn.	${\dot{x}}_{1} = - k x_{1} + λ x_{2} - x_{2} x_{3}$
		${\dot{x}}_{2} = x_{1}$
		${\dot{x}}_{3} = - x_{3} + x_{2}^{2}$
	Descr.	Autonomous dissipative flow