||Population dynamics is an important content in research on ecology. Factors that
affect the fluctuating of populations are many, and time lag is one of them. This work
systematically analyzed the theoretical mechanism and process of intra- and inter-specific
competition. We established the intra- and inter-specific competition models with time
lags and simulated it in computer; And we researched the role of time lag effects on onespecies
population fluctuating and its period, and on two-species competitive population;
We analyzed specific examples. We mainly obtain the following conclusions:
1), By simulating and studying the discrete and continuous intra-specific competition
models with time lags, we find that: time lags are important factor that cause populations
unstable. In general, the longer the time lags, the less stable the populations.
2), By simulating and researching the following discrete models with time lags, we
find that: the number of the populations'''' fluctuating period equates to 4T+2 (T is time
lag), at the same time, we proved that our conclusion of the above is correct at T=1, 2.
Nt+1 = [1:0 ¡ b(Nt¡T ¡ Neq)]Nt
Nt+1 = rNt(1 ¡
3), From the researching on intra-specific competition system with time lags, we can
see that: the influence of time lags are very strong; With the increasing of time lags, large
extent fluctuating will gradually arise for the number of populations; It is also possible
that the periodical fluctuation of the system arise, therefore, the system will gradually
become unstable. Seeing from the cases that the competition coefficients are all bigger
than 1, we can know that, with the increasing of time lags, the strong population with big
competition coefficients can also become weak population and fail to compete with its
4), By researching two dominating sand-fixation plants in sand area, we established
improved intra-specific competition model of plants; We calculated and numerically analyzed
the specific examples; We demonstrated the role and process of intra-specific competition,
and the mechanism of coexistence.
The above results expand the theory of intra- and inter-specific competition, and the
analyzed results of specific examples have application perspective in ecological restoring.