@article{(Open Science Index):https://publications.waset.org/pdf/16095,
	  title     = {Transient Population Dynamics of Phase Singularities in 2D Beeler-Reuter Model},
	  author    = { Hidetoshi Konno and  Akio Suzuki},
	  country	= {},
	  institution	= {},
	  abstract     = {The paper presented a transient population dynamics of phase singularities in 2D Beeler-Reuter model. Two stochastic modelings are examined: (i) the Master equation approach with the transition rate (i.e., λ(n, t) = λ(t)n and μ(n, t) = μ(t)n) and (ii) the nonlinear Langevin equation approach with a multiplicative noise. The exact general solution of the Master equation with arbitrary time-dependent transition rate is given. Then, the exact solution of the mean field equation for the nonlinear Langevin equation is also given. It is demonstrated that transient population dynamics is successfully identified by the generalized Logistic equation with fractional higher order nonlinear term. It is also demonstrated the necessity of introducing time-dependent transition rate in the master equation approach to incorporate the effect of nonlinearity.
},
	    journal   = {International Journal of Industrial and Manufacturing Engineering},
	  volume    = {7},
	  number    = {8},
	  year      = {2013},
	  pages     = {1647 - 1652},
	  ee        = {https://publications.waset.org/pdf/16095},
	  url   	= {https://publications.waset.org/vol/80},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 80, 2013},
	}