Studies On The Dynamic Behavior Of Delay And Non-delay Coupled System

Scholoars and experts have been maintaining a very high level of enthusiasm to the study of dynamic system. The research about it shows that dynamic systems could be coupled by a number of simple subsystems through a certain way. However, as the in-depth study, people find that it becomes more difficult to study those systems when their demensions increase. So there was a idea that whether or not people could study the complex system through subsystems and relations between them, because complex systems could coupled by simple subsystems. What kind of changes and impacts to the system would produce after the coupled. It worths thinking.This paper would study dynamic behavior of the complex systems that coupled by simple subsystems(two or more). So we want to find that subsystems that have different dynamic behavior(stable or unstable), would produce what kind of impacts to the coupled system. First, we intruduce a neural network model, and analyse the big coupled system using different coupling matrix by numberical simulation. We find that the system coupled by some chaotic neural ones would generate steady and periodic behavior. Second, we add delay factor to the above model, and find that the big system also generates steady and periodic behaviors by numerical simulation. At the last, we take the spring oscillator as a example to show the dynamic behaviors of the coupled system. We also find that the coupled spring oscillator has periodic orbit.