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Figure 3 System ( 5.3 ) is global attractive.
By the way, the global attractive property of the solutions is also obtained.
Theorem 2.1 The equilibrium point x ¯ = 0 is global attractive (respectively asymptotically stable) in (1.1) if and only if u ¯ = 0 is global attractive (respectively asymptotically stable) in (2.2).
In [11], Peng discusses global attractive periodic solutions of BAM neural networks with continuously distributed delays in the leakage terms.
Motivated by the above discussion, we will investigate the global attractive sets of the permanent-magnet synchronous motor system.
Many fundamental questions, such as complex chaotic behavior and the existence of a global attractive compact set, are still not solved.
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However, little seems to be known about the global exponential attractive set of chaotic systems [22 24].
But the global exponential attractive sets of systems (2 -(4) are still unknown.
In this section, we will discuss the global exponential attractive sets of PMSM system (2), (3) and (4).
In Section 3, we prove that there exist global exponential attractive sets for the chaotic PMSM system.
Our principal aim here is to investigate the global exponential attractive sets of (2), (3) and (4).
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