The Research On Lagrange Stochastic Stabilization Of Differential Systems

When the system is running, it will be subjected to internal or external random disturbance, which is inevitable. And interference on the system performance will undoubtedly cause certain influence. Therefore, in most cases, it will enhance the robustness of the system to resist the impact of interference on the performance of the system, or filter to reduce or eliminate the interference effect on the system performance. At the same time, there are some research shows that, under certain conditions, random interference can also improve the performance of the system. Especially for some unstable system, using the random disturbance or artificially increasing the intensity of noise can make the system into a stable system, which shows that the random disturbance is not always playing a negative role and effectively using it will help to improve the system performance. So far, relevant theory is also applied to the many practical problems, such as population model, financial models and ecosystem model. This paper makes a study on how to improve the performance of the system by using random disturbance effectively, which based on three hot dynamic systems.1. Multi-agent consistency:First, this paper gives the algorithm of multi-agent consistency including environmental noise. It proposes an stochastic noise control method of adding adaptive activation. By using stochastic noise effectively, stochastic stabilization of the system can be realized. While being proved theoretically, the multi agent system can be randomly and uniformly stabilized when adding random noise which satisfies certain conditions. The effectiveness of this method has been shown through three groups of simulation experiments.2. Gene regulatory networks:This paper studies the stability of the gene regulatory networks and has proved that if adding appropriate stochastic noise for some unstable system, the noise will play a positive role and the stabilization of the system will be achieved. To verify the effectiveness of the new method practically, this paper presents the significant effect of it through simulation.3. Stochastic Chen chaotic system:First, this paper studied the Lagrange stability of Chen chaotic system with stochastic noise and proved that stochastic noise can make the global exponential attractor of the Lagrange stability field for Chen chaotic system smaller than without it. Then it verified the statement through simulation.