TY - JOUR
T1 - DYNAMICS OF POPULATIONS SUBJECT TO SELECTIVE HARVEST
T2 - UNIQUENESS, STABILITY, AND PERIODIC BEHAVIOUR.
AU - Chiang, Anthony S.T.
AU - Thompson, Robert W.
PY - 1986/9
Y1 - 1986/9
N2 - We develop here the criteria for the existence and uniqueness of steady state points, stability of the steady states, and the possibility of periodic behavior of a population, which is governed by a known age-dependent specific reproduction function, and an externally controlled age-dependent removal function. In general, it appears that uniqueness of the steady state is not guaranteed, the steady state points are metastable, and periodicity can arise only if the removal function is periodic or if the removal and maternity functions are periodic. Lastly, we prove the conclusion, previously conjectured by M. E. Gurtin and R. C. MacCamy, that no periodic solution exists for systems having an age-dependent maternity function and a density-dependent removal function.
AB - We develop here the criteria for the existence and uniqueness of steady state points, stability of the steady states, and the possibility of periodic behavior of a population, which is governed by a known age-dependent specific reproduction function, and an externally controlled age-dependent removal function. In general, it appears that uniqueness of the steady state is not guaranteed, the steady state points are metastable, and periodicity can arise only if the removal function is periodic or if the removal and maternity functions are periodic. Lastly, we prove the conclusion, previously conjectured by M. E. Gurtin and R. C. MacCamy, that no periodic solution exists for systems having an age-dependent maternity function and a density-dependent removal function.
UR - http://www.scopus.com/inward/record.url?scp=0022782287&partnerID=8YFLogxK
M3 - 期刊論文
AN - SCOPUS:0022782287
SN - 0368-1653
VL - 17
SP - 295
EP - 302
JO - Journal of the Chinese Institute of Chemical Engineers
JF - Journal of the Chinese Institute of Chemical Engineers
IS - 5
ER -