In this paper, we investigate the finite-time stochastic synchronization problem of two chaotic systems with noise perturbation. We propose new adaptive controllers, with which we can synchronize two chaotic systems in finite time. Sufficient conditions for the finite-time stochastic synchronization are derived based on the finite-time stability theory of stochastic differential equations. Finally, some numerical examples are examined to demonstrate the effectiveness and feasibility of the theoretical results.
In this paper we study the regularity properties of the one-dimensional one-sided Hardy-Littlewood maximal operators M+ and M−. More precisely, we prove that M+ and M− map W¹,p(R) → W1,p(R) with 1 < p < nekonečno, boundedly and continuously. In addition, we show that the discrete versions M+ and M− map BV(ℤ) → BV(ℤ) boundedly and map l¹(ℤ) → BV(ℤ) continuously. Specially, we obtain the sharp variation inequalities of M+ and M−, that is Var(M+(f))<Var(f) and Var(M−(f))<Var(f) if f ∈ BV(ℤ), where Var(f) is the total variation of f on ℤ and BV(ℤ) is the set of all functions f: ℤ → R satisfying Var(f) < nekonečno., Feng Liu, Suzhen Mao., and Obsahuje bibliografii