The Related Extension and Application of the Ši'lnikov Theorem

Table 2

The systems with two equilibrium points.

System	Typical parameter values	The equivalent point	The eigenvalues
Sprott(r)	𝑎=4	(−1,1/4,±1)	−1.6075,0.3038±2.2101𝑖; 1.203,−1.1015±2.3317𝑖
Sprott(g)	𝑎=0.5	(0,0,0); (−2,4,−2)	−1,0.25±0.9682𝑖; 0.2149,−0.3574±2.1274𝑖
Sprott(j)	𝑎=0.3	(0,0,0); (−1/0.3,−1/0.3,1/0.09)	−1,0.15±0.9887𝑖; −0.7868,−0.1066±1.0153𝑖
Sprott(l)	𝑎=1.7,𝑏=1.7	(2.4064,5.7908,0); (−0.7064,0.499,0)	0.4087,−0.7543±2.6547𝑖; −0.4693,0.3179±2.5698𝑖
Sprott(n)	𝑎=2.7	(0,0,0); (−1,0,−1)	−0.5101,0.2551±1.3767𝑖; 0.4315,−0.7157±1.3436𝑖
Sprott(o)	𝑎=2.7	(0,0,0); (1,−1,2.7)	−0.5101,0.2551±1.3763𝑖; 0.3828,−1.1914±1.0121𝑖
Sprott(p)	𝑎=3.1,𝑏=0.5	(0,0,0); (−3.1,−3.1,0)	−1,0.25±1.7428𝑖; 0.8347,−0.6673±1.8079𝑖
Rössler	𝑎=𝑏=0.2,𝑐=5.7	(0.007,−0.0351,0.0351); (5.693,−28.4649,28.4649)	−5.687,0.097±0.9952𝑖; 0.1935,0.068±5.428𝑖
𝜁^3	𝑎=3.5,𝑏=2	(0,0,0); (3.5,0,0)	0.9255,−0.9627±1.6897𝑖; −1.3833,0.1916±1.5791𝑖
Rössler Toroidal	𝑎=0.386,𝑏=0.2	(0,0,0); (0,1.5181,−1.5181)	−0.5071,0.1535±1.064𝑖; 0.4524,−0.3262±1.0903𝑖
BS	𝑎=10,𝑏=13	(±√1.3,∓√1.3,0.1)	−14.4526,1.7263±13.3011𝑖