Global Dynamics of the Chaotic Disk Dynamo System Driven by Noise

Table 1

Ultimate boundary for stochastic dynamo system.

Scopes of stochastic processes	Simulated results of expectation	Theoretical estimates of expectation
−7.692934 ≤ x1 ≤ 7.736921	Ex1 = 0.104873	|Ex1| ≤ 30.026679
−1.484651 ≤ x2 ≤ 2.785851	Ex2 = 0.033916	|Ex2| ≤ 5.011244
1.160790 ≤ x3 ≤ 22.686710	Ex3 = 19.921792	|Ex3| ≤ 30.026679
−1.372995 ≤ x4 ≤ 3.000000	Ex4 = 0.248853	|Ex4| ≤ 5.011244
2.652947 ≤ r1 ≤ 526.916239	Er1 = 410.415404	0 ≤ Er1 ≤ 901.601426
0.000000 ≤ r2 ≤ 13.000000	Er2 = 0.525692	0 ≤ Er2 ≤ 25.112567

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