https://doi.org/10.1140/epjb/e2004-00300-1
The stationary properties and the state transition of the tumor cell growth mode
1
Department of Physics, Yunnan University, Kunming 650091, P.R. China
2
Yunnan Police Officer Academy, Kunming 650223, P.R. China
Corresponding author: a meidch@ynu.edu.cn
Received:
9
February
2004
Revised:
26
June
2004
Published online:
30
September
2004
We study the stationary properties and the state transition of
the tumor cell growth model (the logistic model) in presence of
correlated noises for the case of nonzero correlation time. We
derived an approximative Fokker-Planck equation and the stationary
probability distribution (SPD) of the model. Based the SPD, we
investigated the effects of both correlation strength (λ)
and correlation time (τ) of cross-correlated noises on the
SPD, the mean of the tumor cell population and the normalized
variance () of the system, and calculated the state
transition rate of the system between two stable states. Our
results indicate that: (i) λ and τ play opposite
roles in the stationary properties and the state transition of the
system, i.e. increase of λ can produce a smaller mean
value of the cell population and slow down the state transition,
but increase of τ can produce a larger mean value of the cell
population and enhance state transition; (ii) For large λ,
there a peak structure on both
-λ plot and
-τ plot. For the small λ,
increases with increasing λ, but
increases
with decreasing τ.
PACS: 87.10.+e – General theory and mathematical aspects / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 02.50.Ey – Stochastic processes
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2004