Dynamical Process of Complex Systems and Fractional Differential Equations
Behavior of dynamical process of complex systems is investigated. Speci.cally we analyze two types of ideal complex systems. One is an aggregate composed of many different segments having different time constants, such as concrete and rocks. The other is a network composed of neurons in neural system or brain, where neurons extend their dendrites to their neighboring neurons. It is found that their internal states of the systems are universally expressed by power law distribution. The exponent of the power law distribution is fully determined by the ratio of the parameters characterizing their structures of the systems. Expressed differently the internal states are expressed as the total number of the activated segments or the total number of activated paths on a growing network. We calculate activated states to an external force by specifying a stochastic process. There are three types of behaviors in the response function. they are the power exponential , and stretched exponential functions, determined by the magnitudes of the internal states varying with time. Finally we express the constitutive equation as a simple fractional differential equation(FDE) and give a physical interpretation to the exponent of the FDE.
Ideal complex systems hybrid system power law distribution slow relaxation super slow relaxation
Hiroaki Hara Yoshiyasu Tamura
Tsutumidori-Amamiya,10-21-406, Aoba-ku, Sendai, 981-0914,JAPAN The Institute of Statistical Mathematics, 10-3, Midorimachi,Tachikawa, Tokyo 190-8562 JAPAN
国际会议
The Fifth Symposium on Fractional Differentiation and Its Applications(第五届国际自动控制联合会分数阶导数及其应用会议)
南京
英文
1-6
2012-05-14（万方平台首次上网日期，不代表论文的发表时间）