Bilinear effect in complex systems

¹ Department of Physics and Astronomy, San Jose State University - San Jose, CA 95192-0106, USA
² Department of Modern Physics, University of Science and Technology of China - Hefei 230026, China
³ ADACEL Systems Incorporation - 5945 Hazeltine National Drive, Orlando, FL 32822, USA
⁴ Nanjing Municipal Museum - 4 Chao Tian Gong, Nanjing 210004, China
⁵ Web Sciences Center, University of Electronic Science and Technology of China - Chengdu 610054, China
⁶ School of Visual Arts and Design, University of Central Florida - Orlando, FL 32826, USA

Received: 23 March 2010
Accepted: 13 September 2010

Abstract

The distribution of the lifetime of Chinese dynasties (as well as that of the British Isles and Japan) in a linear Zipf plot is found to consist of two straight lines intersecting at a transition point. This two-section piecewise-linear distribution is different from the power law or the stretched exponent distribution, and is called the Bilinear Effect for short. With assumptions mimicking the organization of ancient Chinese regimes, a 3-layer network model is constructed. Numerical results of this model show the bilinear effect, providing a plausible explanation of the historical data. The bilinear effect in two other social systems is presented, indicating that such a piecewise-linear effect is widespread in social systems.