The Related Extension and Application of the Ši'lnikov Theorem

Table 1

The systems with one equilibrium point.

System	Typical parameter values	The equivalent point	The eigenvalues
Sprott(d)	𝑎=4	(1/4,1/16,0)	−1.937,0.4685±1.3585𝑖
Sprott(e)	𝑎=0.5	(−2,−4,4)	−1.872,0.686±0.7732𝑖
Sprott(f)	𝑎=0.4	(5/2,5/2,−1)	−2.1347,0.3674±0.5775𝑖
Sprott(i)	𝑎=2	(0,0,0)	−1.3532,0.1766±1.2028𝑖
Sprott(k)	𝑎=3.9,𝑏=0.9	(1, 0.9, −39/9)	−1.4333,0.2166±1.6353𝑖
Sprott(m)	𝑎=2,𝑏=2	(−1/4,0,1/2)	−2.3146,0.1573±1.3052𝑖
Sprott(q)	𝑎=0.9,𝑏=0.4	(4/9,0.9,−0.4)	−1.6183,0.3091±0.6787𝑖
Sprott(s)	𝑎=2.017	(0,0,0)	−2.2199,0.1015±0.6635𝑖
Zhou(a)	𝑎1=−1.221,𝑎2=1.5,𝑎3=2; 𝑏=−1.3,𝑐1=−1.5,𝑐2=−1	(−0.281,−1.0201,1.3521)	−1.8716,0.8354±1.3325𝑖
Hc	𝑎=0.25,𝑏=4,𝐹=8,𝐺=1	(7.9679,−0.0065,0.0297)	−0.2498,6.9678±31.8716𝑖