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Number of results

Journal

2013 | 11 | 10 | 1238-1245

Article title

Dynamical process of complex systems and fractional differential equations

Content

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EN

Abstracts

EN
Behavior of dynamical process of complex systems is investigated. Specifically we analyse two types of ideal complex systems. For analysing the ideal complex systems, we define the response functions describing the internal states to an external force. The internal states are obtained as a relaxation process showing a “power law” distribution, such as scale free behaviors observed in actual measurements. By introducing a hybrid system, the logarithmic time, and double logarithmic time, we show how the “slow relaxation” (SR) process and “super slow relaxation” (SSR) process occur. Regarding the irregular variations of the internal states as an activation process, we calculate the response function to the external force. The behaviors are classified into “power”, “exponential”, and “stretched exponential” type. Finally we construct a fractional differential equation (FDE) describing the time evolution of these complex systems. In our theory, the exponent of the FDE or that of the power law distribution is expressed in terms of the parameters characterizing the structure of the system.

Publisher

Journal

Year

Volume

11

Issue

10

Pages

1238-1245

Physical description

Dates

published
1 - 10 - 2013
online
19 - 12 - 2013

Contributors

author
  • Tsutumidori-Amamiya, 10-21-406, Aoba-ku, Sendai, 981-0914, Japan
  • The Institute of Statistical Mathematics, 10-3, Midorimachi, Tachikawa, Tokyo, 190-8562, Japan

References

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Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.-psjd-doi-10_2478_s11534-013-0224-2
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