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Second-order stochastic lattice dynamical systems random attractor

Author: HuangZiQiao
Tutor: LiuYuRong
School: Yangzhou University
Course: Basic mathematics
Keywords: Random attractor Random lattice dynamical systems Slowly increasing collection
CLC: O19
Type: Master's thesis
Year: 2007
Downloads: 45
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Abstract


Random attractiveness as an important class of dynamical properties , because of its wide application , recently more and more attention from researchers . In this article , we mainly study the following second-order lattice dynamical systems random random global attractor existence . First, we establish Hilbert space F = lλ2 × l2, and prove that the random solutions of second-order lattice dynamical systems in the space F = lλ2 × l2 on the existence and uniqueness . Through the solution of the system carried out a global estimate derived equation continuous dependence on the initial value , and then get the above equation can be generated by a continuous random dynamical systems . Then, using stochastic analysis, the equation of the \This yields , the second-order stochastic lattice dynamical systems in the presence of a bounded slowly increasing focus on tight global attractor . The first part is an introduction, describes the background knowledge related to this article ; second part briefly give information about the stochastic dynamic systems concepts and knowledge , while the system ( 1 ) gives a brief description and description ; the third part , we will prove equation ( 1 ) in the solution space F = lλ2 × l2 on the existence and uniqueness ; fourth part , we prove that the system ( 1 ) the existence of absorbing set ; fifth part priori estimates obtained through random dynamical system ( 1 ) random global attractor existence .

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CLC: > Mathematical sciences and chemical > Mathematics > Dynamical systems theory
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