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So in this paper, an adaptive scheme for synchronization of chaotic system with random parameters by using the fuzzy impulsive method and combining the properties of Wiener process and Ito differential is investigated.
The main concepts of this paper are applying fuzzy method to approximate the nonlinear part of system, then using Ito differential to study the Wiener process of random parameters of chaotic system, and realizing synchronization under fuzzy impulsive method.
To illustrate the effectiveness of the synchronization scheme with the modified impulsive controller, using the given parameters in the original impulsive method b p = − 0.8 and b l = 0, one obtains a e α Δ = 0.3228 < 1 according to Corollary 2, which is simulated in Figure 3. Figure 3 The error system with the impulsive interval Δ = 0.09 and N = 0.
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Impulsive methods have been applied in almost every field of the applied sciences.
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A numerical example is also provided to show the effectiveness and feasibility of the impulsive control method.
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