Chaos arising from the discretization of O.D.E. and an age dependent population model.

1983 ◽  
pp. 361-375
Author(s):  
Masaya Yamaguti ◽  
Masayoshi Hata
Keyword(s):  
Population Model ◽  
Age Dependent

HOPF BIFURCATION IN AN AGE-DEPENDENT POPULATION MODEL WITH DELAYED BIRTH PROCESS

2012 ◽  
Vol 22 (06) ◽  
pp. 1250146 ◽  
Author(s):  
PING BI ◽  
XIANLONG FU
Keyword(s):  
Steady State ◽  
Hopf Bifurcation ◽  
Population Model ◽  
Semigroup Theory ◽  
Time Lag ◽  
Population System ◽  
Birth Process ◽  
Birth Function ◽  
Age Dependent ◽  
Dynamical Properties

This paper is devoted to the study of an age-dependent population system with Riker type birth function. The time lag factor is considered for the birth process. We investigate some dynamical properties of the equation by using C0-semigroup theory, through which we obtain some conditions of asymptotical stability and Hopf bifurcation occurring at positive steady state for the system.

A Stochastic Population Model for Managing the Atlantic Menhaden (Brevoortia tyrannus) Fishery and Assessing Managerial Risks

1985 ◽  
Vol 42 (8) ◽  
pp. 1371-1379 ◽  
Author(s):  
D. Ruppert ◽  
R. L Reish ◽  
R. B. Deriso ◽  
R. J. Carroll
Keyword(s):  
Population Model ◽  
Atlantic Menhaden ◽  
Juvenile Growth ◽  
Fishing Mortality ◽  
Brevoortia Tyrannus ◽  
Estimation Errors ◽  
Age Dependent ◽  
Stochastic Recruitment ◽  
Stochastic Population Model

A model including an age-structure, a stochastic egg-recruitment relationship, density-dependent juvenile growth, age-dependent fishing mortality, and fecundity dependent upon size as well as age was used to investigate three types of harvesting strategies: constant yearly catch policies, constant fishing mortality rate policies, and "egg escapement" policies, which are defined in the article. Because of stochastic recruitment, constant yearly catch policies appear unsuitable for managing Atlantic menhaden (Brevoortia tyrannus). Both other types of policies are suitable, but the egg escapement policies have higher long-term average catches. Using decision theory, we investigated risks due to the randomness of recruitment and to the estimation errors for the biographical parameters in our model. The risks appear to be acceptable.

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