TY - JOUR
T1 - Nonlinear character dependent models with constant time delay in population dynamics
AU - Castillo-Chavez, Carlos
N1 - Funding Information:
The main ideasi n this paper are part of my Ph.D. dissertationa t the University of Wisconsin-Madison under the supervisiono f Fred G. Bauer. This work was partially supportedb y Simon A. Levin and his National ScienceF oundationG rant DMS-8406472I. thank thema ll. Finally, I thank Morton E. Gurtin for his inspiringp aper (with R. C. MacCamy), and for his not objectingt o my borrowings omeo f his expositorys tyle.
PY - 1987/11/15
Y1 - 1987/11/15
N2 - A nonlinear character dependent model with constant time delay that extends the linear model of W. S. C. Gurney and R. M. Nisbet is introduced as a result of making the birth and death moduli dependent upon the total population. We reduce this model-an initial boundary value problem-to the solution of a pair of coupled nonlinear functional equations. Under suitable conditions, we establish the local existence, uniqueness, and continuation of solutions for all positive time. We also establish necessary and sufficient conditions for the local stability of time independent solutions in the form of a Lotka type characteristic equation similar to M. E. Gurtin and R. C. MacCamy's charateristic equation arising from their nonlinear extension of the age dependent MacKendrick-Von Foerster model.
AB - A nonlinear character dependent model with constant time delay that extends the linear model of W. S. C. Gurney and R. M. Nisbet is introduced as a result of making the birth and death moduli dependent upon the total population. We reduce this model-an initial boundary value problem-to the solution of a pair of coupled nonlinear functional equations. Under suitable conditions, we establish the local existence, uniqueness, and continuation of solutions for all positive time. We also establish necessary and sufficient conditions for the local stability of time independent solutions in the form of a Lotka type characteristic equation similar to M. E. Gurtin and R. C. MacCamy's charateristic equation arising from their nonlinear extension of the age dependent MacKendrick-Von Foerster model.
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U2 - 10.1016/0022-247X(87)90211-3
DO - 10.1016/0022-247X(87)90211-3
M3 - Article
AN - SCOPUS:45949118684
SN - 0022-247X
VL - 128
SP - 1
EP - 29
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -