Stochastic and Fractional Differential Equations: Attractor, Invariant Measure and Their Relationship

Dear Colleagues,

Mathematical models that study the evolution of many natural phenomena such as astroscience, fluid mechanics, plasma physics, and weather change are often nonlinear evolution equations and resulting infinite dimensional dynamic systems. However, in real life, the development of something is sometimes influenced by accidental random factors. Many studies have shown that due to the interaction between noise and nonlinearity, the system structure may be completely destroyed, making the system change from ordered to disordered, or vice versa. Therefore, it is necessary to study infinite dimensional random dynamic systems. The study of infinite dimensional random dynamical systems requires the combination of knowledge of dynamical systems, partial differential equations, fractional differential equations, functional analysis, stochastic analysis, and the complexity of their own problems. Currently, this is still in the initial and innovative stage.

The focus of this Special Issue is to continue to advance research on topics relating to the theory and application of infinite dimensional random dynamical systems. Topics that are invited for submission include (but are not limited to):

1. Random attractors of stochastic and fractional differential equations;
2. Invariant measures of stochastic and fractional differential equations;
3. The relationship between random attractors and invariant measures;
4. Stability of stochastic complex systems.

Prof. Dr. Dingshi Li
Dr. Chunmei Zhang
Guest Editors

Manuscript Submission Information

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